The delay dashed the hopes of advocates who had sought prompt action on a bill already passed by the House of Representatives that would ensure protection for same-sex and interracial marriages.
The move came after weeks of closed-door talks between a small group of Democratic and Republican senators who looked at ways to amend the House bill in order to attract at least 10 Republican supporters who would join 48 Democrats and two independents.
The U.S. Census Bureau in 2019 estimated that there were 543,000 same-sex married couple households and 469,000 households with same-sex unmarried partners living together.
Senate Majority Leader Chuck Schumer is "extremely disappointed" that there were not at least 10 out of 50 Republicans willing to come forward to support the gay rights legislation, spokesman Justin Goodman said in a statement.
Goodman added that Schumer nonetheless is "100% committed" to holding a vote this year. Schumer had hoped to set up a first procedural vote on the legislation on Monday.
Senators leading the negotiations issued a statement saying that they needed additional time to work on the bill. "We are confident that when our legislation comes to the Senate floor for a vote, we will have the bipartisan support to pass the bill," said Democratic Senators Tammy Baldwin and Kyrsten Sinema and Republicans Susan Collins, Rob Portman and Thom Tillis.
Earlier, Baldwin told reporters that a bill will be put to a vote following the elections.
Joni Madison, the interim president of LGBT civil rights organization Human Rights Council, called for the bill to be brought to the floor for a vote "at the earliest possible moment," calling the delay disappointing.
"Marriage equality - for both LGBTQ+ and interracial couples - is not and should not be a partisan issue, and to treat it as such is an insult to the millions of families who are impacted," Madison said in a statement.
The thinking behind the delay is that following the midterm elections Republican senators will feel freer to back the legislation at a time when any voter backlash would be two years away with the next elections.
"If they think that improves their chances of passage, that's their prerogative," Republican Senator John Cornyn told reporters, adding that he would vote against a bill codifying same-sex marriage into law.
The Senate's failure to win sufficient Republican support for a bill came after the Democratic-controlled House of Representatives in mid-July passed such a measure with the backing of 47 Republicans.
Schumer has been careful to give negotiators -- and wavering Republicans -- the space they needed to put together a bill that would succeed, rather than just force senators to go on record for or against but result in a failed vote.
Over the past several days, the small group of senators and their staffs worked on an amendment designed to protect the "religious liberty" concerns of some Republicans.
But some supporters of the bill said the real snag was that there just were not enough Republicans willing to back any such bill, especially six weeks before the elections.
"The Republicans need to stand up and explain why they don't want to vote for equality among all human beings and the right to marry the person you love," Democratic Senator Elizabeth Warren told reporters upon hearing about the delay.
Republican Senator Rob Portman told reporters, "We were very, very close" to moving toward passage of a bill.
The push to enact a federal law recognizing gay marriage arose after conservative U.S. Supreme Court Justice Clarence Thomas in June wrote that the same logic that led the court to overturn the national right to abortion could also lead it to reconsider its earlier decision legalizing same-sex marriage.
Early on, Senator Mitt Romney was one of several Republicans saying there was no need to tackle such legislation after the Supreme Court ruled in 2015 that the right to marry is guaranteed to same-sex couples.
The court in 2015, however, was markedly less conservative than the current high court.
Supporters of the legislation fear that the delay - the second in two months - could see support further erode, especially if Republicans win in November elections.