The measure requires all states to recognise same-sex marriages.

It is a relief for hundreds of thousands of couples who have married since the Supreme Court's 2015 decision that legalised those marriages and have worried about what would happen if the ruling were overturned.

The US president invited thousands to celebrate at the White House on Tuesday as he signed the Respect for Marriage Act, including politicians from both parties.

He was also joined by first lady Jill Biden and Vice President Kamala Harris and her husband, Doug Emhoff.

A long-time advocate for gay rights, singer Cyndi Lauper, performed at the event.

"For once, our families, mine and a lot of my friends - and people you know, sometimes your neighbours - we can rest easy tonight, because our families are validated," the singer said at the White House briefing room before the ceremony.

Meanwhile, Senate Majority Leader Chuck Schumer said he would wear the same purple tie to the ceremony that he wore to his daughter's wedding. His daughter and her wife are expecting their first baby next spring.

"Thanks to the dogged work of many of my colleagues, my grandchild will live in a world that will respect and honour their mothers' marriage," he said.

The new law aims to safeguard gay marriages if the US Supreme Court ever reverses Obergefell v Hodges, its 2015 decision legalising same-sex unions nationwide.

It will also protect interracial marriages after the Supreme Court in Loving v Virginia struck down laws in 16 states barring interracial marriage in 1967.

Mrs Biden tweeted a nighttime photo of the White House after the historic day.

In a statement last week, Mr Biden said: "Congress has restored a measure of security to millions of marriages and families.

"They have also provided hope and dignity to millions of young people across this country, who can grow up knowing that their government will recognise and respect the families they build."

Tuesday's signing marks the culmination of a months-long bipartisan effort sparked by the Supreme Court's decision in June to overturn Roe v Wade - the 1973 ruling that made abortion available across the country.

It also points to another chapter in Mr Biden's legacy on gay rights, as he has pushed to expand LGBT+ rights since taking office.

During a television interview in 2012 when he was vice president, he memorably endorsed same-sex unions.

Days later, President Barack Obama announced he was also a supporter of gay marriage.

When he became president, Mr Biden reversed Donald Trump's efforts to strip transgender people of anti-discrimination protections.

Attendees at Tuesday's ceremony were given a card commemorating the president's comments from his 2012 interview.

"What this is all about is a simple proposition: Who do you love?" he said on NBC's Meet The Press a decade ago.

"Who do you love, and will you be loyal to the person you love? And that is what people are finding out, is what all marriages at their root are about."