A senior Reagan administration official predicted today that the Soviet Union and the United States will reach an interim agreement this fall to limit the number of medium-range nuclear missiles they each base in Europe.

The official, who traveled here from Washington with Defense Secretary Caspar W. Weinberger, said that he envisions an agreement under which the United States would begin deploying its new Pershing II and cruise missiles in western Europe as scheduled in December but would restrict their number in return for Soviet reductions.

However, he stressed that such an agreement can be achieved only if the Soviets are convinced that the United States will otherwise go forward with full deployment. To keep them thinking that, he said, requires that NATO countries remain united behind the deployment decision.

If they do, he said, "I think we'll have an agreement by the fall."

Weinberger, who is beginning a week-long series of meetings with NATO and military officials in West Germany, Belgium and Norway, declined to predict when or whether an agreement might be reached. He said only that all the missiles will be deployed on schedule, barring an agreement with the Soviets to do otherwise.

He also said that insistence by Soviet leader Yuri V. Andropov on including British and French nuclear weapons in the intermediate nuclear force (INF) negotiations at Geneva would be "simply a way of bringing the discussions to a halt, because he knows there is no way the British and French weapons can be included in this discussion."

During Weinberger's meetings here, as at the Williamsburg economic summit, European officials, who have encountered heated popular opposition to the missile deployment, are expected again to urge American flexibility in the INF and the strategic arms reductions talks (START) with the Soviet Union.

In a related matter, Weinberger himself said the Soviets have responded favorably to President Reagan's proposal to improve the quality of the "hot line" between Washington and Moscow. But the Soviets do not seem interested, Weinberger said, in other "confidence building" measures Reagan proposed recently to reduce the possibility of accidental nuclear war.

Those measures included cooperation against terrorist activities, regular meetings between Soviet and U.S. military officers and increased diplomatic links. "Their basic response to that was they thought what we had was a pretty good system," Weinberger said, based on recent meetings he held with Soviet Ambassador Anatoliy F. Dobrynin.

The hot line teletype was installed 20 years ago and transmits messages slowly. "We can sit there typing out a couple of passages from the Bible and Karl Marx, and it takes a very long time to work things out," Weinberger joked. He called upgrading of the hot line "a very real possibility," which could be accomplished a few months after an agreement to do it.

The problem of nuclear missiles in Europe is stickier, Weinberger said. The NATO nations agreed in 1979 to deploy the new missiles in response to Soviet deployment of intermediate-range SS20 missiles aimed at western Europe.

Last week, the Soviets threatened to base more nuclear missiles in eastern Europe if NATO goes ahead with its plan. Despite the harshness of the Soviet rhetoric, administration officials traveling here tended to dismiss the threat, saying that the Soviets have mid-range nuclear missile launchers in East Germany and are trying to disrupt NATO.

Weinberger said in response to a question that deployment of the U.S. missiles is "not inevitable."

"But we are all fully prepared: the manufacturing process, the testing process are moving ahead on schedule," he said. "If there is not an agreement, we are fully prepared to go ahead with the scheduled deployment on schedule."