WASHINGTON (Reuters) - U.S. President Joe Biden signed a sweeping new border measure on Tuesday that would allow authorities to quickly deport or send back to Mexico migrants caught crossing the southwestern border if the daily number of crossings exceeds 2,500.

Biden took office in 2021 vowing to reverse some of Republican Donald Trump's restrictive policies but grappled with record levels of migrants caught crossing illegally, which has become an issue in the tight rematch against in November's presidential election.

Some human rights activists and left-leaning immigration experts were sharply critical of the measure, while Republicans said it did not go far enough or was too late.

AMY FISCHER, MIGRANT RIGHTS, AMNESTY INTERNATIONAL

"This executive action plays into false narratives about invasions at the border and advances a policy grounded in white supremacist ideas at the expense of people in search of safety in the U.S....This is an utterly shameful move for a country that once helped draft the Refugee Convention."

UNITED NATIONS SPOKESPERSON FLORENCIA SOTO NINO

"Access to asylum for those in need is paramount and any person who claims to have a well-founded fear of being persecuted in their country of origin should have access to safe territory and have this claim assessed before being subjected to deportation or removal."

ARIZONA REP. RUBEN GALLEGO, DEMOCRAT

"Today's announcement is a step in the right direction, but we still have more work to do. We also need to hire more border patrol agents, fix our broken asylum system, and keep our communities safe."

US REPUBLICAN PRESIDENTIAL CANDIDATE DONALD TRUMP

"Biden is pretending to finally do something about the border--but in fact, it's all for show because he knows we have a debate coming up in 3 weeks."

TEXAS SENATOR TED CRUZ, REPUBLICAN

"He could have stopped this every single day of his presidency...What the White House is doing today is they're just playing a political game."

SILKY SHAH, DETENTION WATCH NETWORK

"Biden is using the same legal authority to justify his order that Trump used in 2017 for the 'Muslim Ban.' We were outraged then and we are outraged now - particularly as Biden has completely abandoned the values he once touted of implementing a 'fair and humane' immigration system that helped him get elected."

(Reporting by Heather Timmons; Editing by Alistair Bell)