The Republican-controlled Senate, in another blow to the New Right's agenda of social issues, yesterday summarily killed legislation aimed at permitting organized prayer in public schools.

The proposal, sponsored by Sen. Jesse Helms (R-N.C.), was rejected, 62 to 36, after brief debate. It was a low-water mark for backers, who had formerly commanded a majority vote and hours of Senate deliberation.

Helms' bill would have removed the prayer issue from federal court jurisdiction, giving state and local governments power to allow prayers in schools if they chose to do so.

Controversy about the so-called "court-stripping" provision complicated the issue, undercutting support for Helms' proposal among conservatives and liberals.

"Did you really write this bill?" Helms was asked by Sen. Barry Goldwater (R-Ariz.), who said it was tantamount to "outlawing the Supreme Court." Adding that he was "kind of surprised" that Helms wrote the bill, Goldwater said, "If I wrote it, I would be ashamed."

Similar legislation was thwarted by a filibuster in 1982, when it attracted as many as 54 votes but fell short of the 60 needed to halt debate. Last year, the Senate voted, 56 to 44, for a constitutional amendment to allow spoken prayers in public schools -- 11 votes short of the two-thirds majority needed for passage of an amendment.

President Reagan has supported a constitutional amendment to allow for a moment of silent prayer in school, and two of his Cabinet officials recently urged new debate on the issue of separation of church and state.

Sen. Lowell P. Weicker Jr. (R-Conn.), who has led the fight against prayer measures over the years, said after yesterday's vote that it signaled waning public support for religion-related crusades of the New Right.

"The more times it's voted on, the more times the television preachers talk about what Congress ought to do, the more people realize it's these people [the New Right] who are bringing government into religion, and they don't want it," he said.

Helms brushed off the significance of declining support for prayer measures in the Senate, saying, "That's the way the cookie crumbles." He said he brought the measure up yesterday primarily to force a recorded vote the issue. "I imagine people in the evangelical movement are going to be willing to circulate it," he said.

Although Republicans hold a 53-to-47 Senate majority and many were elected with support from the religious right, Helms disputed the idea that the Senate is friendly turf for conservative causes.

"This is a liberal Senate. It is under control of Republicans, but it's not a conservative Senate," he said.

Such other New Right causes as abortion and school busing have been receding as issues on Capitol Hill, although antiabortion riders have been added to foreign aid bills and the abortion controversy is holding up House action on a major civil rights bill, largely because of fears that it could force Catholic hospitals to perform abortions.

The prayer vote followed about 40 minutes of desultory debate preceding formal introduction of the measure. Under prior agreement, the Senate leadership moved for an immediate vote, leaving some senators clutching remarks that had to be inserted, undelivered, in the Congressional Record. The 1982 debate lasted about six weeks.

A narrow majority of Republicans supported the Helms proposal, while most Democrats voted to scuttle it. Maryland senators opposed the measure; Virginia senators supported it