The Reagan administration, anticipating possible Libyan reprisals, fine-tuned security precautions at home and abroad yesterday. But U.S. officials and terrorism experts said any Libyan moves are not likely for two or three months and almost certainly would be directed against American targets overseas.

There are about 3,500 Libyans in this country and, according to a high-level intelligence estimate made two years ago, that number includes approximately 200 "fanatic" followers of Libyan leader Muammar Qaddafi.

Most official concern yesterday focused on the possibility of terrorist actions overseas. Several State Department officials privately agreed with a comment by Robert Kupperman, an analyst at Georgetown University's Center for Strategic and International Studies who specializes in terrorist behavior. He said:

"The logistical problems of trying to hit us here in the United States are too difficult. I think we're going to see a lot of renewed terrorist activity, but it probably will be aimed at American embassies, businesses and individuals in Europe and the Middle East. And it probably won't happen for two or three months when we begin to tire of our current high state of vigilance and Qaddafi has had a chance to regroup the terrorist organizations, like Abu Nidal, that work with him."

State Department officials said U.S. embassies and other outposts were warned last Friday that security threats could arise from the U.S.-Libyan confrontation in the Gulf of Sidra.

They said the warning was prompted by concern both about Libyan-inspired terrorist attacks and possible violent demonstrations by Arab masses outside of Libya angered by an alleged U.S. attack on an Arab state.

"We've had indications in the last few months of possible Libyan surveillance at some of our overseas installations, and we have to assume that if Qaddafi intends to retaliate, his best riposte would be a foreign outpost," said one senior department official, who declined to be identified.

But he added that there are no plans to caution U.S. citizens against traveling abroad.

Pentagon sources said that bodyguards had been assigned to Navy Secretary John F. Lehman Jr. and Adm. James D. Watkins, chief of naval operations, because of unspecified internal "threats."

The Federal Aviation Administration also announced that it was increasing airline and airport security.

Officials of federal agencies primarily charged with countering foreign threats -- the FBI, the Secret Service, the Immigration and Naturalization Service and the Customs Service -- said that heightened security measures have been in effect for a long time and that no dramatic new precautions were being contemplated.

The Libyan community in this country has been under surveillance since 1981 when the administration said it had reason to believe that Qaddafi was sending a team of assassins here. Although the FBI refuses to discuss its operations, it maintains an around-the-clock watch, aided by electronic surveillance, on the Libyan mission at the United Nations and specific places such as a McLean residence that houses a large number of Libyan students.

Verne Jervis, a spokesman for the Immigration and Naturalization Service, said that about 3,500 Libyans, about half of them students and the others tourists or business people, are believed to be in the country. However, other officials said that number probably has decreased considerably since January, when the administration imposed sanctions that cut off business dealings with Libya and made it more difficult for students to get funds.

Jervis said the majority of Libyan students are in Sun Belt states such as Texas, Florida and California. Almost all have their expenses paid by the Libyan government, and a "threat assessment" made for the administration by the intelligence community in 1984 said there were "approximately 200 fanatic pro-Qaddafi students in the United States" at that time