In further retaliation for the Soviet downing of a South Korean airliner last week, President Reagan yesterday ordered that both U.S. offices of the Soviet airline Aeroflot be closed, that their three officials be sent home and that U.S. airlines stop selling tickets in this country even for connecting flights with Aeroflot.

The president's order followed quick approval yesterday by the Civil Aeronautics Board of his request for a number of actions against the Soviet airline, the largest in the world.

The CAB, in voting 4 to 0 to approve the president's proposal, went a step further and urged American travel agents to observe voluntarily "the letter and spirit" of these actions, a move that could cut down on U.S. agencies' booking of passengers on Aeroflot flights by instead using other foreign or American airlines.

The president's actions marked the second time this week he has moved to impose some penalties on the Soviet Union for shooting down the Korean Air Lines jumbo jet last Thursday after it strayed into Soviet airspace.

All of the sanctions thus far, including those announced yesterday, have been widely viewed as limited in scope. Because of this, Reagan has come under sharp and steady criticism from some conservative groups, and from some other sectors as well, to take stiffer action, including cancellation of recent agreements to sell the Soviets grain and pipe-laying equipment, and of arms talks between the two nuclear superpowers.

White House spokesman Larry Speakes said that the latest moves are "in no way in response to public pressure."

He described them as part of what the administration has called "a measured response" to the "brutal and unprovoked Soviet attack" on KAL Flight 007.

Aeroflot flights to and from the United States have been prohibited since Jan. 5, 1982, as part of the administration's response to the Soviet-supported crackdown on the Polish trade union movement.

The moves announced yesterday are intended to isolate the Soviet carrier further by making it harder to book connecting flights with American airlines or to be sure of baggage arrangements.

Speakes said that the economic impact of the latest moves on Aeroflot is hard to estimate, especially since American use of the airline was curtailed sharply already. But he said the move is intended to "cost them prestige and, to some extent, foreign exchange," and to encourage other countries to follow suit.

"It is our hope that if other nations will step in and do the same thing, this would have a profound effect," Speakes said.

Administration officials said that Transportation Secretary Elizabeth Hanford Dole has cabled 17 countries seeking support for a resolution of condemnation at the forthcoming International Civil Aviation Organization (ICAO) meeting in Montreal and suggesting denial of landing rights and a prohibition on inter-airline ticketing.

The president acted on his own authority in giving Aeroflot until Sept. 15 to close its offices in New York and Washington and have its officials depart. Soviet Ambassador Anatoliy F. Dobrynin was informed of this action by Undersecretary of State Lawrence S. Eagleburger.

Since the 1982 ban on Aeroflot flights to this country the two offices have been involved mostly in booking connections with Aeroflot flights in Canada and other countries. Canada this week announced the suspension of landing rights for Aeroflot for 60 days.

Last year, administration officials said, about 20,000 passengers, some of them Americans, flew Aerflot between Montreal and Moscow. The officials also said that, despite the ban on flights to this country, a significant amount of Aeroflot's business originates in the United States.

The moves requested by Reagan and approved by the CAB yesterday include:

* Suspending Aeroflot's right to sell tickets in this country.

* Prohibiting U.S. airlines from selling tickets in the United States for transportation on Aeroflot.

* Precluding U.S. airlines from carrying traffic to, from or within the United States where an Aeroflot flight is on the ticket.

Directing U.S. airlines to suspend any interline service arrangements with Aeroflot (officials said this means such things as baggage transfers).

Prohibiting U.S. airlines from accepting any tickets issued by Aeroflot for air travel to, from or within the United States.

These measures will take effect on Monday.

The White House statement said "the duration of these measures . . . will be . . . in part dependent upon the extent to which the U.S.S.R. demonstrates its willingness to honor essential standards of civil aviation, makes a full account of its shootdown of the airliner and issues an apology as well as compensation to aggrieved parties."

There were 269 people, including 61 Americans, aboard the Boeing 747.

Speakes said Reagan will attend a memorial service for the victims today at noon at the Washington Cathedral, but aides said the president has decided not to attend another service on Sunday at the invitation of Kathryn McDonald, whose husband, Rep. Larry McDonald (D-Ga.), was among those killed.

As officials explained it, the actions announced yesterday would not prevent someone in this country who wants to travel to Moscow from going to a foreign airline office and booking passage, say from New York to London on the foreign airline and from London to Moscow on Aeroflot. A U.S. travel agent could do the same, as well as book an Aeroflot connection with an American flight, but they are being asked not to do so.

Officials said the ban also does not rule out an American airline ticket office overseas from issuing a ticket in which one of the legs of the journey involves Aeroflot so long as the flight does not begin or end in the United States.

Officials said they did not want to get into legal issues of extra-territoriality with friendly governments at this time, so extending the ban to cover these other aspects was not attempted at this time.

In New York yesterday, Cord Hansen-Sturm, vice president of General Tours, the leading organizer of tours from the United States to the Soviet Union, told the Associated Press that U.S. tourist agencies will not be significantly hurt by Reagan's request. He said most U.S. tourist agencies have no direct contact with Aeroflot.

The new White House moves came after a lengthy and frosty meeting between Secretary of State George P. Shultz and Soviet Foreign Minister Andrei A. Gromyko in Madrid where both are attending a conference. Shultz said later that Gromyko had given a "totally unacceptable" explanation of Soviet actions in the downing of the plane.

In a related development, Speakes indirectly confirmed a report by a New York Times columnist that a U.S. RC135 reconnaissance plane was off the Soviet coast in international airspace on the same night as the ill-fated Korean airliner because the Air Force plane was trying to monitor an upcoming Soviet missile test.

The Soviets use the Kamchatka Peninsula region, over which the Korean plane strayed, as an impact area for missile tests. The test reportedly did not occur, and U.S. officials said yesterday they didn't know which of their missiles the Soviets had planned to test fire.