President Reagan's charge that Soviet secret agents were sent to help instigate and foster the American nuclear freeze movement is proving to be an embarrassment for his administration.
For one thing, the Federal Bureau of Investigation apparently can do no more than show that the Soviets have tried to influence the movement, not that they have had any real impact in either starting the movement or keeping it going.
In the view of some officials, the President's charge has served only to divert attention away from the real issues involved in the nuclear freeze debate. These officials are beginning to hope that the question of Soviet influence will simply fade away. As they see it, with or without the Soviets and their agents of influence, the freeze movement would probably be about where it is today.
These same officials, who request anonymity, distinguish between the peace and nuclear-freeze movements in Western Europe and those which parallel them in the United States. They say they think Soviet influence has been much greater in Europe.
In October 1981, for example, according to the State Department, the Danish government expelled, because of improper conduct, a KGB (Soviet secret police) officer. No such case has come to light in the US.
''There is documentary evidence that the Soviets have tried to influence the European movement,'' said one Reagan administration official.
''In the United States, the movement is influenced not by the Soviets but by radical American leftists,'' the official continued. ''That influence ranges from the 'Hollywood Left' . . . to the left wing of the Democratic Party. I don't see communists behind it.'
Other officials defend Reagan and his allegations by noting that he has classified intelligence available to him which cannot be made public. But the administration official said: ''I've seen the same stuff the President has . . . It's been a strictly ad-hoc reaction on his part. It's understandable given his particular world outlook. . . . But I wish he'd never gotten into it.'
Reporters have pressed the White House to provide evidence of Soviet influence on the freeze movement. On Nov. 12 Larry Speakes, the deputy White House press secretary, provided a list of government reports and magazine articles. But the State Department reports mentioned by the White House deal only with European and international movements. An October Reader's Digest article shows that Soviet officials and others, described as KGB agents, attended some peace and freeze-movement meetings and indicates that they made statements which impressed some Americans. It does not demonstrate any significant Soviet impact on the movement as a whole.
The reaction of the FBI to queries about Soviet influence in this country has been cautious. FBI officials state that the Soviets have ''targeted'' the American peace movement, but decline to go into detail. They say that the Permanent Select Committee on Intelligence of the House of Representatives will soon be releasing a lengthy report on Soviet secret activities which is based in part on FBI testimony, and that this should help people understand the issue.
On Nov. 16, at an Atlanta press conference, FBI Director William H. Webster was asked how the Soviets might try to influence the movement to freeze nuclear weapons. Mr. Webster said the Soviets ''have engaged in what is called active measures by which they seek to bring about a psychological effect on various movements that are consistent with their overall world objectives and strategies and this is no exception.''
The reaction from sponsors of nuclear freeze resolutions has been sharp. Jan Kalicki, an aide to Sen. Edward M. Kennedy (D) of Massachusetts, who has been the cosponsor of the most highly publicized resolution on the subject, said of Reagan's allegations: ''Is the President saying that the Soviets have manipulated the Catholic bishops, city and county councils, and state legislatures across the country?''
Mr. Kalicki said that allegations of Soviet influence may first have been made in order to dissuade those tempted to vote for freeze referendums in the Nov. 2 election.
Sen. Mark Hatfield, a Republican from Oregon, has sponsored, together with Mr. Kennedy, a resolution calling for a verifiable freeze on the testing, production, and deployment of nuclear weapons by the US and the USSR. The administration charges that such a freeze would leave the Soviets ahead of the US in nuclear weapons because the Soviets have been building and deploying such weapons faster than the US has.
Mr. Hatfield has challenged the administration to produce names of KGB agents who have helped instigate the freeze movement. An aide said Hatfield consulted with no one other than four staff members when he first introduced a nuclear moratorium amendment to the SALT II Treaty in 1979.
''I haven't seen any KGB people under my sofa,'' said Hatfield.