The rash of terrorist-linked incidents in the past two weeks -- and a presidential warning about security problems at the Athens airport -- have raised concerns among Americans going abroad this summer about their personal safety while traveling.

Travel agents and tour operators both locally and nationally say they have received numerous calls from customers scheduled to depart soon for Europe -- and Greece in particular -- who want to know if they should go. Some travelers have canceled their trips outright. But according to these travel industry sources, most people who booked a foreign vacation are going ahead with their plans, and by the week's end cancellations seemed to be tapering off.

There is no firm figure for overall cancellations, but they probably number into the thousands nationally, based on estimates from several tour operators. Industry sources consider the drop-offs worrying but, in fact, negligible compared to the more than 6 million Americans expected to travel to Europe this year.

While large numbers of Americans continued to flock to Europe, the State Department, as of Friday, was still advising travelers that "an above average potential for terrorist activity exists" at the Athens airport.

The State Department's Citizens Emergency Center, which has been flooded with calls from apprehensive travelers, says, "Our purpose is to provide information so people can make an informed decision. It's not to say 'yes' or 'no' whether they should go."

The State Department customarily issues advisories on dangers or other problems Americans might encounter in a foreign country.

Meanwhile, the Federal Aviation Administration last week ordered U.S. airlines to strengthen security procedures at airports in reaction to the Athens airport hijacking, the Air-India crash and terrorist bombings at the Tokyo and Frankfurt airports. As a result, passengers and their baggage are going to be more closely scrutinized at airport check-in on selected domestic and international flights.

And the international travel industry, faced with a crisis in what had shaped up to be a record-breaking summer for U.S. tourists in Europe, has scrambled to make adjustments in tour itineraries and taken other steps to try to keep cancellations at a minimum.

For example, TWA Getaway, the nation's largest organizer of tours to Europe, changed its 17-day Rome-to-Athens "Islands of the Mediterranean Cruise" to a 15-day Rome-to-Rome round trip among the islands because of customers' worries about flights home from the Athens airport.

Some (but certainly not all) tour operators are waiving at least a part of any cancellation penalties for people who choose not to go ahead with a trip for which they have paid.

Faced with this basically unsettled situation, how can apprehensive travelers reach what ultimately must be a personal decision on whether to travel?

Consult with your travel agency. Agents can tell you how much of a cancellation penalty, if any, you will incur if you decide not to go, and they may be able to book you on an alternate tour.

Keep abreast of the news so you can make an informed judgment.

Check with the State Department's Citizens Emergency Center (202-632-5225). The center can advise not only on potential political or terrorist dangers, but also on hotel-room shortages and health concerns.

Consider, if you think you will be nervous traveling abroad, whether you really will enjoy the vacation.

Here is a closer look at the current international situation as it affects vacation travelers:

New airport security: The FAA last week ordered U.S. airlines to immediately intensify security procedures at airports, including increasing the screening of passengers and baggage on selected flights. Most of the attention will be focused on international flights.

The new procedures are expected to lengthen the lines at some security checkpoints, so foreign-bound passengers should arrive at the airport with sufficient time to spare. Check with the airline close to your departure date for guidance on how early to arrive at the airport.

Among the new security procedures:

Passengers boarding international flights will no longer be able to check luggage at curbside check-in counters. It must be taken (by you or by a skycap) inside to the main airline check-in desk.

Security personnel will inspect some hand-carried luggage that has already passed through the X-ray machines. Passengers carrying wrapped or sealed packages could be asked to open them.

Passengers and their checked baggage will be matched to assure that the passenger who checks luggage actually boards the flight. No unaccompanied baggage will be flown unless it is inspected or X-rayed.

Athens flights: Pan Am yesterday resumed its daily flight from the United States to Athens (with a change of planes at Frankfurt). The flight was halted following President Reagan's Athens airport warning.

Pan Am's decision to resume was based, says spokesman Merle Richman, on "the improved security posture which has developed in the past week" at the Athens airport.

TWA, which continued operating its daily flight, did so because, says spokesman David Venz, "Our bookings tell us Americans still want to go to Greece. And we had already flown a lot of people to Greece, and they were expecting those red and white planes to fly them home again."

Cancellations: Many Americans are canceling their foreign travel plans, especially to Athens; others are altering European itineraries to avoid Athens; and some are postponing departures, waiting to see how the air safety situation develops.

But most foreign-bound Americans appear to be embarking on their trips as planned; and there are even a few who had not previously booked trips but are now doing so.

The American Society of Travel Agents conducted "an informal survey" of 100 travel agents across the country last Tuesday (following the Air-India crash), and most reported that they actually were getting fewer calls than expected, says ASTA spokeswoman Linda Burnett.

In the first few days after the hijacking of Trans World Airlines Flight 847 in Athens, TWA Getaway tours experienced what spokesman Venz calls a "quite noticeable" number of cancellations of tours to Greece. In the past week, the situation "has stabilized." The cancellations to other European destinations were "negligible."

American Express, another major U.S. tour operator, reports a "significant" number of cancellations on trips to Greece but to no other destination in Europe. And the number of calls about Greece is declining. Spokeswoman Miriam Trokan says some customers are rebooking on other European tours; some are adopting a "wait and see" attitude"; and since Monday, "a few who had canceled here called back to rebook to Greece."

The third of the three major U.S. transatlantic tour operators, Globus Gateway/Cosmos Tourama of Forest Hills, N.Y., has gotten "several hundred" cancellations to Europe, says executive vice president Jeffrey Joseph, a number he considers "disturbing" although it actually represents "less than 1 percent" of the firm's tour business abroad. The firm expects to take 20,000 travelers to Greece this summer and many more thousands to the rest of Europe.

At the moment Joseph is optimistic, but like other tour operators he is troubled by what might happen to the international travel scene if another terrorist incident occurs this summer. And at least one tour operator is factoring into its plans for next year the possibility of a cutback in European travel because of the terrorist threat.

Between 10 and 15 families booked with one Washington travel agency have canceled trips to India as a result of the Air-India crash. Laxmi Chand, president of World Wide Travel, which specializes in travel to India, says he also has switched some passengers from Air-India to Pan Am.

A New York spokesman for Air-India says the line, which flies daily from New York via London, has received "scattered cancellations, but flights are still going pretty full."

There is some feeling in the travel industry that cancellations are coming mostly from first-time travelers to Europe, who may have been experiencing normal pretrip jitters before the terrorist incidents. Cancellations seem to be heaviest for package tours and tours combined with cruises.

Cancellation penalties: Travelers canceling trips because of concern about the international situation may face substantial financial penalties, especially those due to depart in the next week or two. However, some travel suppliers are refunding deposits and waiving any penalties.

Travelers could lose some or all of their deposits for organized tours, hotels and cruises; or they could incur an airline penalty of $50 to $75 if they canceled a 21-day advance-purchase ticket on a scheduled airline. This penalty is being waived for most Athens-bound flights.

"Basically, a lot of suppliers have been running business as usual," says Nancy Baria, manager of consumer affairs for the American Society of Travel Agents. "It's a tough situation. It's not as if Americans have been prohibited by law from those countries. If their clients cancel, then their clients are going to suffer cancellation penalties."

Passengers on charter flights stand to lose the entire cost of their transatlantic ticket unless it can be resold. The 100 percent penalty is standard for charter cancellations within 30 to 45 days before a flight.

"Unless the State Department bans travel, we cannot allow passengers to cancel," says Evelyn Kirouac, vice president of Wainwright Travel, a Bethlehem, Pa., charter firm offering six charters a week to Europe. Der Tours of Santa Monica, Calif., a German-owned charter operator flying weekly to Europe from 11 U.S. cities (including Baltimore/Washington), agrees. "Our position is that there is no threat whatsover to our passengers," says marketing director Rick Weber.

Other travel suppliers are less stringent.

American Express says "up to this point" nobody canceling has been penalized. TWA Getaway says its tour customers can switch from an Athens itinerary to another European tour without a penalty; and they can cancel a tour to Greece altogether and get a full refund except for hotel costs. TWA is currently negotiating with the hotels for refunds of these deposits, which would be returned to the customer.

Sun Line Cruises, which operates two luxury liners out of the Athens port of Pireaus, says it has waived penalties for canceling any of its cruises through Aug. 2. This permits passengers scheduled to sail before then to postpone making a decision without losing any of their reservation payment. Sun's hope is that the Athens airport problems will be resolved quickly and that any currently doubtful passengers with later sailing dates will decide to join the cruise.

However travel agents express it, the basic advice they are giving their clients is that the decision rests with the individual traveler.

"Flying is still the safest way to travel," says Scott Lynch, owner of Springfield Travel Service of Springfield, Va., who nevertheless tells clients "it's their judgment call. We wouldn't want to lead them in one direction or another."

At Van Slyke and Reeside Travel, a Washington travel agency specializing in independent travel abroad, vacation supervisor Pat Lohaus tells worried callers: "You can't be thinking in terms of a trip you're going to be nervous about. It will ruin the trip."

But, she adds, "Our personal feeling is that security at all airports abroad has tightened to such a degree that they are truly safer than before. Most of our clientele are very experienced travelers . They realize the risk of driving in the car five miles from home is greater."