The United States publicly urged Israel and Syria yesterday to "exercise restraint" to avert a new missile crisis between them, while State Department officials said prospects for a clash on the issue appear to be diminishing.

The public statement by State Department spokesman Charles Redman followed almost four weeks of secret U.S. diplomacy involving the two Mideast antagonists, according to official sources. "We don't think either country is anxious for a fight," said a State Department source familiar with the U.S.-Israeli-Syrian discussions.

The possibility of a major Israeli-Syrian clash emerged from a Nov. 19 incident in which Israeli warplanes on a reconnaissance mission over Lebanon downed two Syrian MiG23s that challenged them.

The Israeli jets flew into Syrian airspace to down the Syrian jets in the dogfight, prompting Damascus to announce its "legitimate right to respond decisively" to what it termed an "act of aggression." Within days, the Syrians deployed mobile SA6 and SA8 antiaircraft missiles in Lebanon and more powerful SA2 antiaircraft missiles in three previously prepared positions just inside Syrian territory at the Syrian-Lebanese border.

Tension mounted in Israeli governmental and military circles because of the threat posed by the newly deployed missiles to Israeli reconnaissance flights and other potential military operations. Nothing was said publicly until Sunday, however.

The growing danger of a clash was strikingly reminiscent of the "crisis of the missiles" over Syrian antiaircraft deployments in Lebanon, which raged for almost 14 months in 1981-82. The earlier episode engaged the United States in extensive but unsuccessful shuttle diplomacy involving a special U.S. envoy, Philip C. Habib, and ended with destruction of the Syrian missiles on the third day of Israel's invasion of Lebanon.

Unlike in the previous crisis, this time neither Syria's missile deployments nor Israel's demand for their removal became public immediately. U.S. officials said this development, which may have involved Israeli censorship, provided time for quiet diplomacy before national prestige and passions became deeply engaged.

The U.S. role this time was enhanced because the State Department's senior Mideast official, Assistant Secretary Richard W. Murphy, happened to be in the area on other business. Murphy was in Israel Nov. 21, in Damascus Nov. 29 and back in Israel Dec. 3-5. A former U.S. ambassador to Syria, Murphy is said to be an unusually effective U.S. channel to Syrian President Hafez Assad.

The Syrian mobile missiles in Lebanon were withdrawn after U.S. diplomats passed word to Damascus that the Nov. 19 air action did not signal any change in Israeli military policy and that the violation of Syrian airspace had been a mistake, according to U.S. sources. Similar Syrian antiaircraft missiles mounted on halftracks have been taken in and out of Lebanon on several occasions in the past three years, the sources said.

The antiaircraft missiles just inside Syrian territory remain, despite U.S. appeals that Syria return to the "pre-Nov. 19 status quo" by removing them, the officials said.

There is no indication now that Syria is preparing to remove the SA2 missiles that were recently deployed, according to the officials. The fact that these weapons are in Syrian territory complicates the case for their removal, especially after attention was drawn to them by Israeli public statements starting last weekend, the sources said.

U.S. sources took encouragement, however, from the latest Israeli declarations, which they took to be an effort to avert a crisis. The officials said Syria may find a way over time to ease Israeli concerns if there are no further complications.