President Carter, appealing for the votes of women and new Yorkers, received a badly needed boost in this pivotal state today from a cheering crowd of several thousand union members who gave him his most enthusiastic reception of the campaign.

Waving Carter signs and singing their union's theme song "Look For the Union Label," members of the International Ladies," Garment Workers Union turned their annual convention into a Carter rally after hearing the president accuse Ronald Reagan and other Republicans of having "turned their backs on American women."

The President later promised New York business and labor leaders he will continue to support federal loan guarantees to the city as he chided Reagan for once having said, "I have included in my morning and evening prayers every day the prayer that the federal government not bail out New York City."

According to Carter campaign officials, Reagan made the remark in a speech in late 1975 when he was preparing to challenge then-President Ford for the Republican presidential nomination. Now, however, Reagan is trying to broaden his base of support. With an eye on New York's rich lode of 41 electoral votes, the GOP nominee softened his opposition to federal aid to New York over the weekend, asserting that he opposed a pending Senate amendment that would cost New York $300 million annually.

But like many things Reagan has said during more than two decades as an advocate of conservative causes, the remark was thrown back at the former California governor today by the Carter campaign.

"I don't think the people of New York are going to pay much attention to candidates who make positive statements only for a few weeks during an election year," the president said.

New York's prize of 41 electoral votes -- second only to California's 45 -- is what brought Carter this morning to the state considered essential to his reelection. In a contest against a conservative Republican from the West, New York normally would be considered natural Democratic territory. But Carter has problems here with disaffected liberals and Jews, and is particularly threatened by the candidacy of independent John B. Anderson, who has been endorsed by New York's Liberal Party.

In a recognition of the importance of the Jewish vote here and of the suspicions many Jews harbor toward administration policies, the president departed from the text of his speech to the ILGWU convention to reaffirm United States opposition to any attempt to expel Israel from the United Nations.

There have been reports that Arab and other Third World nations may challenge Israel's credentials at the current session of the U.N. General Assembly. Such a move, if successful, "would raise the gravest questions about the further participation of the United States and other nations in the deliberations of that body," Carter said.

The ILGWU was among the president's strongest supporters during the Democratic primaries and its members greeted him today with a display of enthusiasm rarely seen in the Carter campaign.

Basking in the applause that repeatedly interrupted his speech, the president muted his recent harsh criticism of Reagan's foreign policy positions to warn the union members of the domestic consequences of a Reagan victory.

Carter made his strongest appeal to the union convention on the issue of the Equal Rights Amendment, which Reagan opposes.

"The new Republican leaders have turned their backs on American women," he said. "Some of them say they are not opposed to women's rights. They just want to let the states do it.

"That's what the enemies of womens' suffrage said 70 years ago. 'Leave it to the states,' That's what the enemies of civil rights said 20 years ago, 'Leave it to the states."'

From the cheering of the ILGWU convention, Carter went to a meeting of New York business, labor and political leaders.

He jabbed mildly at Reagan's foreign policy rhetoric, accusing him of "repeatedly" advocating that the United States engage in "ill-considered, unnecessary interventions around the world."

But the message likely to do the president the most political good with the city leaders was his pledge of a continued flow of federal loan guarantees in new guarantees that are currently tied up in Congress, the same measure backed by Reagan.