The United States and the Soviet Union, in a moment of renewed superpower tension in the Middle East, have taken a new step toward negotiated curbs on medium-range nuclear missiles, State Department officials said yesterday.

Secretary of State Alexander M. Haig Jr. and Soviet Ambassador Anatoliy F. Dobrynin, in a previously unannounced meeting that lasted an hour, tackled both the Mideast and arms issues at the State Department Firday night, according to U.S. sources

The Haig-Dobrynin exchange, in the view of State Department sources, constituted the start of "preliminary discussions" on curbing medium-range missiles in Europe.

Haig promised the North Atlantic Treaty Organization Council this month in Rome that such discussions would begin promptly, looking toward a more definitive meeting in September with Soviet Foreign Minister Andrei Gromyko. The Haig-Gromyko meeting, in turn, is to make plans for the opening of formal negotiations on the issue by the end of the year.

NATO agreed in December 1979 to deploy new U.S. missiles in Europe, but only on the condition that negotiations on control of those weapons go forward at the same time.

The Reagan administration has been unenthusiastic about arms control discussions with the Soviets until the United States has taken steps to improve its relative military position. Nevertheless, the administration agreed to pursue the Euro-missiles talks promptly in deference to the European allies.

The most pressing item on the superpower agenda, the volatile confrontation between Israel and Syrian military forces around Lebanon, was also discussed by Haig and Dobrynin. State Department sources said there is no clear indication that the Russians will act to defuse the crisis as it heads into a particularly dangerous period.

The top echelon of the administration has been engaged in a round of particularly urgent meetings in the past several days based on the perception that, as Haig said publicly last Thursday, "time is lrunning out" on envoy Philip Habib's peace mission.

Several officials suggested that a period of maximum danger is expected to begin on Monday if no solution is in prospect. It was unclear whether this assessment is based on specific information from Israel, which has threatened to bomb the Syrian missile sites in Lebanon.

There is growing concern within the top ranks of the administration that an Israeli-Syrian clash could seriously jeopardize U.S. interests in the Middle East, especially in the event that the military action is not strictly limited to the Syrian anti-aircraft missile sites.

While the Soviet Union might reap advantages from the U.S. difficulties and from a chance to play a larger role in the region, Moscow is also believed to be reluctant to become involved in a clash with extremely dangerous potential.

According to a State Department analyst, the Soviets have cautioned Syria in recent days not to get into a war with Israel over Lebanon, but at the same time made it clear that Moscow would provide support if Syria is attacked. Specifically, it is believed that the Russians have promised to replace any Soviet-built surface-to-air missiles destroyed by Israeli air attack.

In the meeting with Dobrynin, Haig also discussed the plight of imprisioned Soviet dissident Anatoliy Shcharansky, whose wife, Avital, visited Haig last Wednesday. State Department sources said the secretary of state presented a copy of a Senate resolution adopted Tuesday saying that Shcharansky's life is threatened and calling for his release.

Dobrynin, according to the State Department account, rejected these representations as interference in Soviet domestic affairs.

Haig, speaking yesterday to the graduating class of Hillsdale, Mich., College, dropped from his prepared text about American self-confidence a lengthy paragraph describing the Soviet Union as a failing society "confronted by a broad range of troubles, all of them serious." A similar passage in a Haig speech a week ago brought an angry retort from Moscow.