WASHINGTON (AP) _ A homosexual rights group wants the Supreme Court to rule that the government is being discriminatory in blocking them from using ''Gay Olympics'' as the name of their athletic competition.

The Supreme Court agreed Monday to decide the case, in which lower courts have so far blocked San Francisco Arts and Athletics from using the word Olympics. The justices will study whether the United States Olympic Committee and the International Olympic Committee have exclusive trademark control over the term Olympic.

The gay group argues that other organizations have frequently used the name Olympic for various competitions without being prosecuted.

In other action, the high court:

-Agreed to decide whether the free speech rights of a public clerk-typist in Houston were violated when she was fired for saying she hoped someone assassinates President Reagan.

-Refused to revive a Paducah, Ky., ordinance declaring any business a public nuisance if it engages primarily in selling or showing obscene material.

-Rejected a challenge to the Reagan administration's action in January 1984, with the support of Congress, to establish full diplomatic relations with the Vatican.

-Agreed to decide in an Oklahoma case whether railroads may be forced to pay proportionally higher state property taxes than other businesses.

-Refused to shield the daughter of former Philippines President Ferdinand Marcos from imprisonment for refusing to cooperate in a federal investigation of alleged bribery of Philippine officials by U.S. arms dealers.

-Agreed to examine the public's right of access to private beachfront property in California.

San Francisco Arts and Athletics organized the first ''Gay Olympics'' in 1982, prompting Olympic officials to file a lawsuit.

A federal judge ordered the gay group to drop the word ''Olympic'' from the title of its quadrennial sports competition. The organization called the second such event Gay Games II when 3,500 athletes gathered last August in San Francisco. The next competition is planned for 1990.

The 9th U.S. Circuit Court of Appeals ruled in January that the Amateur Sports Act of 1978 gives the U.S. Olympic Committee exclusive control over commercial use of the term Olympic and related symbols in the United States.

The appeals court rejected the gay group's arguments that the law is intended solely to prevent groups unaffiliated with the Olympics from deceptively claiming Olympic sponsorship.

The San Francisco Arts and Athletics group, which is not affiliated with the Olympics, makes no such claim, but said it is a victim of unconstitutional discrimination because many other groups not connected with the Olympics use the term without legal challenge.

''There are competitions throughout the United States called Olympics for firefighters, drinkers of alcohol, senior citizens, crab cookers, chili makers, baby diaperers and Armenians, to name a few,'' lawyers for the gay rights group said.

One question posed by the case is whether the U.S. Olympic Committee, a private group that receives federal aid, is a government entity capable of violating someone's constitutional rights.

The appeals court said the committee is not acting in place of the government and therefore cannot be sued for rights violations.

The appeals court added: ''The word Olympic and its associated symbols and slogans are essentially property. Such property rights can be protected without violating the First Amendment'' guarantee of free speech.

The Supreme Court's ruling in the case, which is expected by next July, will be its second involving gay rights in a year, after it refused for 18 years to consider any homosexual rights controversy.

Last June, the court upheld a Georgia sodomy law that makes homosexual conduct among consenting adults a crime.