The Democratic mayors of New York City and Washington DC are calling on the Biden administration to address what they say is a surge of migrants seeking asylum after travelling from Republican-controlled border states to their cities.

Washington Mayor Muriel Bowser and New York Mayor Eric Adams, both Democrats, have been plunged into a debate over migrants who appear at the US-Mexico border who then take up an offer of state-funded bus trips to the two larger cities after their release by federal immigration authorities. 

Mr Adams criticised the tactic that has been employed by Texas Governor Greg Abbott and Arizona Governor Doug Ducey, both Republicans. 

"The mere fact that they sent people out of their states, people who were seeking refuge in our country, then sent them away — did they deny that?" he asked.

Mr Abbott and Mr Ducey have trumpeted the bus trips, which have been running for months.

While they have been big on political theatre, the trips have fallen short on impact. 

Despite this, Ms Bowser and Mr Adams's calls have put US President Joe Biden on notice about the impact of border enforcement, eliciting gleeful reactions from Republicans who say their pleas are evidence of an immigration crisis.

Asylum seekers are being 'tricked'

Since April, about 5,200 migrants have been bussed away from Texas and, since May, more than 1,100 from Arizona.

The governors said the practice was a voluntary free ride that helped asylum seekers get closer to family and their support networks.

However, Ms Bowser said asylum seekers were being "tricked" because many do not arrive at their final destinations and some were being ditched at Washington's Union Station, near the US Capitol and the White House.

The Washington Mayor wants the federal government to help provide financial support for those seeking asylum. 

In a letter to Ms Bowser, the city's council said volunteer groups were "burned out and overwhelmed".

"Now that the border has come to DC, it is our responsibility to meet the moment," the letter said. 

Council members also castigated Mr Abbott and Mr Ducey for showing "no regard for people who are exercising their human right to seek asylum".

Republicans on the House Homeland Security Committee — who have been critical of the White House — were unable to contain their glee on social media. 

"Looks like Mayor Bowser is starting to feel a glimpse of what it's like to be a border community under the #BidenBorderCrisis."

Help needed for 'unprecedented surge'

In a post on Twitter, Mr Ducey seized on Mr Adams's false claim that Arizona was bussing migrants to New York, instead suggesting they were only being sent to Washington.

"Mayor Adams needs to get his facts straight and pay closer attention to what's really occurring, because our nation's security depends on it," he said. 

On Thursday, Mr Adams further emphasised the influx of migrants into New York and said the city had a legal and moral obligation to provide people shelter, while also condemning Texas and Arizona.

"We do need help from the federal government, through FEMA, to assist us," he said.

"This city was already dealing with a shelter population, and we're going to need help to deal with this unprecedented surge."

Earlier this week, White House press secretary Karine Jean-Pierre said the Biden administration was looking into the mayors' concerns.

She said it was "shameful" for governors to use migrants as "a political tool, as a political play".

$4.3 billion security fails to stem flow 

In Texas, Mr Abbott has cast himself as a counterweight to Mr Biden on immigration, insisting "every American community is a border community".

Mr Abbott's bus rides reveal the aggressive expansion of his immigration enforcement powers into the traditional domain of the federal government.

This month, he authorised state forces to stop migrants and return them to the US-Mexico border, where Texas has spent more than $US3 billion ($4.3 billion) in state funds on security infrastructure, without stemming the flow of migrants.

About one in four migrants named New York as their destination, one in five named New Jersey, while others say they were headed to Georgia or wanted to stay in Washington. 

In June, Border Patrol stopped migrants nearly 193,000 times, marking the first decrease in four months. 

The numbers highlight how little impact the bus rides have had on overall migration flows into the US, which has been the top destination for asylum seekers since 2017, according to the United Nations. 

Mr Adams said New York had experienced a "sharp increase" in asylum seekers — about 2,800 people in recent weeks — but acknowledged the city had no specific data on migration status.

He wanted an investigation into whether other states are directing asylum seekers to New York.

ABC/AP