West Foreign Minister Hans-Dietrich Genscher and Secrtary of State Alexander M. Haig Jr. yesterday agreed on the need to resume negotiations with Moscow on limiting medium-range nuclear missiles based in Europe and that consultations with allies on how to go about this should move ahead rapidly.

The officials' comments, made in the White House yesterday, mark the first positive sign since the Reagan administration took office that some form of arms control talks with the Soviet Union may soon begin to take shape.

At the same time, President Reagan disclosed that he had received a "quite lengthy" letter from Soviet President Leonid I. Brezhnev in which Brezhnev elaborated on the various suggestions for handling East-West issues he had made in a Moscow speech last month, including one for an early summit meeting with the new American leader.

Though the letter reportedly contained nothing new, it is believed to represent the first direct substantive communications between the two leaders. The heads of other Western countries received letters also.

Haig's comments on the need to reopen the U.S.-Soviet talks on European-based missiles, which have been in recess since the preliminary round of discussions in Geneva ended last November, will undoubtedly be welcomed in West Germany. The government of Chancellor Helmut Schmidt has been under heavy pressure from the leftwing of Schmidt's Social Democratic Party to back out of the pledge to allow new U.S. missiles on German soil unless the arms talks with Moscow to limit such weapons on both sides move ahead.

The North Atlantic Treaty Organization agreed in December 1979 to accept the new U.S. missiles -- which will not be in place for another two years -- as a counter to almost 200 Soviet missiles in place. It was also agreed to begin arms talks with Moscow at the earliest date on limiting both deployments to the minimum possible.

Haig and the West Germans have made clear they have no interest in a Moscow proposal for a moratorium on further deployment of such weapons because that proposal would leave Moscow with a big lead in weapons already in place.

But Genscher said that he and Haig agreed that both aspects of the NATO decision -- the new U.S. arms as well as the talks with Moscow -- "should consistently be implemented. We are convinced," Genscher said, "that talks between the U.S. and U.S.S.R. should be resumed in Geneva without delay."

Though it was not clear if Genscher was referring to both countries or just West Germany, Haig added that the United States had always accepted the dual obligations of the NATO decision and that "the problem now is to proceed rapidly, in consultation with our allies, as to how those talks can be carried forward in Geneva or elsewhere if necessary with a view towards implementing" the requirement for talks.

Officials said privately that, assuming the Soviets would come to the bargaining table, it was only a question of timing with respect to when the talks resume.

West German officials said later they were "quite hopeful" that a meeting of NATO's Standing Consultative Group would take place this month at which the Western plan for negotiations would be discussed.

Genscher, speaking through a translator, said he also "welcomed the fact that the U.S. expressed a general readiness and willingness to negotiate in all fields and at all levels," remarks that suggest Haig may have given him some private indication of whether the United States may eventually move to resume arms control talks with Moscow on larger, ocean-spanning strategic nuclear weapons.

Genscher said Bonn would meet its defense commitments to NATO; other West German officials said that recent talk of defense spending cuts in Bonn involved stretch-outs of longterm projects rather than cancellations.

Genscher and Haig had warm praise for each other.Both officials are central to ironing out differences between the United States and its most important military and economic ally in Western Europe. Haig is a former NATO commander and the Europeans look to him as one who can understand their political realities. Genscher is also the leader of the small but powerful centrist Fee Democratic Party that enables Schmidt to rule in a coalition government and that also provides an added element of conservatism to the government on key issues