The U.S. Embassy today formally requested from Poland's martial law authorities increased security protection following a wave of anti-Western vandalism that has coincided with deteriorating diplomatic relations.

The American request was delivered in a diplomatic note handed to the Foreign Ministry by Charge d'Affaires Herbert Wilgis. The note drew attention to more than 20 recent anti-American incidents including attacks on diplomatic vehicles, break-ins at embassy apartments and the daubing of paint on official American buildings in Warsaw.

A U.S. Embassy spokesman said that the embassy received a telephone call yesterday threatening further action against American property. The male caller, who spoke in English, refused to identify himself but implied that the incidents were intended as a demonstration of support for the Palestine Liberation Organization.

The embassy spokesman refrained from saying who he believed was responsible for the vandalism, and insisted that the diplomatic note should not be described as "a protest." In private, however, diplomats do not hide their belief that the incidents have been officially inspired or, at the very least, officially condoned.

Similar acts of vandalism have been directed against other Western embassies whose governments have criticized what they see as repression in Poland. A spokesman for the French Embassy said that paint daubing of French property and damage to embassy vehicles occurred earlier this week. Moreover, two anonymous phone calls were received threatening to kidnap children attending the French school.

The officially controlled Polish news media have complained about a series of anti-Polish "excesses" in both France and the United States in recent days. Official commentators have expressed particular outrage at President Reagan's off-the-record description of the Polish leaders as "a bunch of lousy bums" and a remark by French Prime Minister Pierre Mauroy depicting Poland as a country occupied by its own Army.

The attacks on U.S. and French property in Warsaw can be seen on one level as part of a trivial diplomatic game of tit-for-tat following demonstrations in America and France in support of the banned Solidarity trade union. The difference, however, is that in security-conscious Soviet Bloc capitals anti-Western protests rarely take place without some form of official encouragement.

U.S. diplomats noted that this week the official Polish government spokesman declared that Polish national feelings had been hurt "by official U.S. declarations insulting to the Polish authorities." Within 36 hours of his statement, the U.S. Trade Center and Agricultural Office here had been daubed with a swastika and the letters PLO.

Three U.S. Embassy vehicles were daubed with yellow paint Wednesday night outside a diplomatic apartment bloc, and one other car had its tires slashed.

The U.S. spokesman said that, during his one-hour meeting at the Foreign Ministry, Wilgis received assurances that the Polish authorities were doing everything in their power to protect foreign diplomatic missions. The head of the protocol department, Henryk Laszczyk, was quoted as adding, however, that complete protection for embassies was impossible anywhere in the world.

Meanwhile, it was announced that the military council of the Soviet-led Warsaw Pact defense alliance has wound up three days of talks in Warsaw. No reason for the meeting was given, but it was assumed that the security situation in Poland was among the subjects discussed.

The meeting took place under the chairmanship of the Soviet commander of the pact, Marshal Viktor Kulikov, who was a frequent visitor to Poland during the weeks preceding the imposition of martial law last December.