A federal appeals court ruled on Thursday that Texas can keep the floating barriers it set up to deter migrants from crossing the United States-Mexico border river Rio Grande.

The 5th US Circuit Court of Appeals issued the temporary stay to the order made on Wednesday by Federal District Judge David A. Ezra, but did not provide further details.

On Wednesday, Ezra had ordered that Republican-led Texas must remove the floating barriers by Sept 15 at its own expense and stop building further obstructions in the river.

Texas Governor Greg Abbott's office immediately appealed Ezra's ruling, saying that the state "is prepared to take this fight all the way to the US Supreme Court".

The administration of President Joe Biden filed a lawsuit against Texas in late July, alleging that Texas and its governor violated the Rivers and Harbors Appropriation Act by building a structure in US waters without permission from the US Army Corps of Engineers.

The state argued that the barrier is not a structure that requires authorization and that it notified the International Boundary and Water Commission, the binational body that regulates the Rio Grande, before the installation.

The Mexican government has repeatedly condemned the establishment of water barriers in the Rio Grande as a "violation of our sovereignty".

Meanwhile in New York on Wednesday evening, Mayor Eric Adams told a town hall meeting in Manhattan that the ongoing migrant crisis "will destroy New York City".

"What happened? It started with a madman down in Texas, decided he wanted to bus people up to New York City," Adams said in reference to Abbott sending migrants on buses to New York, Los Angeles and other cities.

The New York Times reported on Thursday that the number of migrants offered free passage from Texas over the past year is a fraction of those who regularly make their way from the southern border to cities around the country.

According to demographers' estimates, of roughly 11 million undocumented immigrants living in all states, most began new lives with a trip from a border city or airport usually paid for by a relative, an aid group or their own savings — not the Texas governor, the Times reported.

Adams said more than 110,000 asylum-seekers have arrived in the city since April last year.

He said the crisis is financially crippling and is creating a $12 billion budget deficit. "We have to feed, clothe, house, educate the children, wash their laundry sheets, give them everything they need, healthcare," Adams said.

Xinhua and agencies contributed to this story.