The Senate yesterday approved legislation aimed at deterring foreign diplomats and their families from using diplomatic immunity to escape prosecution for serious crimes committed in the United States.

While stopping short of denying immunity, the measure spells out new procedures that could limit its use and ease frictions in cities such as Washington and New York, where immunity has been invoked to block prosecution in cases ranging from parking violations to assault and rape.

Among the measure's provisions is one that requires a country's foreign minister to make a specific request for immunity in cases involving crimes of violence, drunken driving or other such serious offenses. Now, immunity is automatically assumed.

In addition, if a U.S. law enforcement body wants to prosecute the individual, the U.S. secretary of state would have to request that a foreign government waive immunity for the accused person. Should the foreign government not waive immunity, the United States would expel the individual as persona non grata. Anyone leaving the United States under these circumstances would be barred from reentry.

The proposal, advanced by Sen. Jesse Helms (R-N.C.) with support of senior Democrats on the Senate Foreign Relations Committee, is a modified version of a stronger measure that Helms proposed earlier that would have excluded all but a relatively few top diplomatic and consular officials from immunity protections.

While it is considered unlikely to satisfy fully either the State Department or local prosecutors, the legislation could have a "significant deterrent and remedial impact without violating established principles of diplomatic immunity," said a spokesman for the Foreign Relations Committee.

It was approved by voice vote as part of a $3.6 billion State Department authorization bill for 1988 that was subsequently passed by the Senate 85 to 5. The authorization measure now goes to conference with the House, which earlier approved a $3.9 billion version. The Reagan administration had requested $4.5 billion and complained that congressional levels were inadequate to finance State Department and related activities for the year.

In other action on the bill, the Senate:Voted to require the Soviet Union to relocate its new embassy complex in Washington from Mount Alto to a lower-elevation site that would be less well-suited for electronic surveillance. The embassy provisions, which also include a demand for renegotiation of the U.S.-Soviet treaty under which both countries are building new embassies in each other's capitals, were previously approved as part of a defense authorization bill that has been threatened with a presidential veto. The State Department bill is considered more likely to be signed into law. Reduced to $50 million the $500 million proposed by the Foreign Relations Committee to reopen 10 U.S. consulates closed for lack of money and to delay for 180 days a committee-proposed prohibition on closing more consulates. Ordered the government to close the New York as well as Washington offices of the Palestine Liberation Organization (PLO). The State Department recently ordered closed the PLO's Washington office, but its New York office is still open. Reversed itself and voted to bar the establishment of an official Washington residence for the secretary of state, which Secretary George P. Shultz has requested for his successors. Voted to prohibit expulsion from the United States of individuals seeking asylum from communist countries, an action prompted by a 1985 incident involving Miroslav Medvid, who jumped twice into the Mississippi River from a Soviet merchant ship and was twice turned back by U.S. immigration officials. Voted to put a ceiling on salaries of U.S. ambassadors so their cumulative annual pay would not exceed the $89,500 salary of members of Congress. Helms won approval of the ceiling after citing a recent report that 307 ambassadors and other high-level State Department employes were earning in excess of $100,000 a year, including incentive payments. Went on record opposing inclusion of the Soviet Union in any Middle East peace conference unless the Soviets reestablish full diplomatic relations with Israel and "substantially" increase the number of exit visas granted to Jews who have applied for emigration to Israel.

Senate approval of the new diplomatic immunity rules followed a 48-to-46 vote last month to reject the stronger Helms measure, which would have denied immunity except for diplomats and consular officials, plus 5,000 family members and staff members of diplomatic missions.