VIENNA, JUNE 28 -- A resolution passed yesterday by a regional branch of the Socialist Party calling for Austrian President Kurt Waldheim to resign has presented Socialist Chancellor Franz Vranitzky with a political headache.

The resolution, by the influential Viennese Socialists at their regional party convention here, may be a first indication that allegations about Waldheim's wartime activities could threaten the country's ruling coalition.

Vranitzky and Socialist Party leader Fred Sinowatz unsuccessfully tried to head off the resolution, saying it would bring on a "state crisis." The Socialists and their conservative People's Party coalition partners had reached an agreement not to officially censure Waldheim, a People's Party member.

The resolution said Waldheim was failing to perform his constitutional duties, because revelations that he served during World War II in a German Army unit that committed war crimes were preventing him from representing the country.

Near diplomatic isolation has surrounded Waldheim since he was elected president a year ago amid allegations that he was implicated in war crimes. Last week, he made his first official visit abroad since becoming president, a trip to Vatican City to meet with Pope John Paul II.

Foreign Minister Alois Mock, who is also leader of the People's Party, said he did not see the coalition endangered by the resolution because it did not reflect Socialist thinking at the national level. But he warned that the Socialists were "moving toward the left."

The strength of the coalition could be tested if other factions of the Socialists begin to call for Waldheim's resignation.

A Gallup Poll last week said 61 percent of Austrians support Waldheim, while 33 percent say he should resign.

Waldheim defeated the Socialist candidate, Kurt Steyrer, last year for the largely ceremonial six-year post.

Waldheim has repeatedly denied that he was involved in war crimes.