The chief diplomats of the United States and East Germany met here today for the first time in six years for a discussion described by the State Department as "warm and cordial" and possibly the opening round of a more extensive dialogue.

Secretary of State George P. Shultz later told reporters it was "a positive meeting," though he tempered the unusually cordial official U.S. description by saying, "I don't have my hat in the air or anything."

The meeting of Shultz and East German Foreign Minister Oskar Fischer, like Shultz's sessions Monday with Romanian and Hungarian foreign ministers, was part of a U.S. effort to improve relations with Soviet allies in Eastern Europe. These and some other Warsaw Pact countries have displayed increasing differences with Moscow on a variety of issues.

According to Shultz, his meeting with the East German uncovered "a mutual desire to work at the relations between our countries" and included discussion of some of the problems.

A State Department announcement said Shultz and Fischer discussed trade, scientific, technical and cultural relations as well as human rights and broad international issues. Among the steps that would improve relations, Shultz said, would be East German action to resolve Jewish claims arising from the Nazi era.

The State Department said it is "pleased by the willingness of East Germany to make progress" in its bilateral relations with West Germany. Officials said there was no direct mention of East German leader Erich Honecker's decision early last month, under heavy Soviet pressure, to postpone an official visit to West Germany.

Shultz said today that it is unlikely that he will travel to Eastern Europe this year, as was being considered some weeks ago.

Shultz said the initiation of an expanded U.S.-Soviet dialogue, which he and President Reagan discussed last week with Soviet Foreign Minister Andrei A. Gromyko, awaits further study by officials in both capitals.

Shultz said he expects the U.S. study to be completed "quite promptly" and the two nations to begin "a process of mutual appraisal" of the Gromyko talks "fairly soon." No new indications have been received from Moscow, he said.

On other subjects, Shultz told reporters:

*At least "some understanding" among the concerned parties about security arrangements in southern Lebanon following an Israeli withdrawal would be important to long-range stablity there. If security arrangements could be worked out, he suggested, "a different situation" regarding Israeli forces in Lebanon could emerge even without agreements with greater political and diplomatic content.

*The United States continues to support the Contadora process of seeking a regional treaty to resolve differences in Central America as one that has made "tremendous strides." He added that some parts of the draft treaty by the four-nation group "represent a problem" in the U.S. viewpoint, but he commended the current process of receiving comments on the treaty draft in hopes of refining it to the satisfaction of all concerned.

*U.S. discussions with Nicaragua, which he related to the Contadora treaty, on the whole have been "businesslike and staightforward." Two senior State Department officials, Langhorne A. Motley and Harry W. Shlaudeman, met here Thursday night with Nicaraguan junta leader Daniel Ortega, but the U.S. side would give no details.