Los Angeles' mayor has accused Texas of a "despicable stunt" after dozens of migrants were driven to the California city from the border.
A group of 42 people, including some children, arrived in Los Angeles on Wednesday afternoon.
Texas' Republican governor defended the move, saying towns in his state were "overwhelmed" because of Democratic President Joe Biden's border policies.
Texas began sending buses of migrants to major US cities last year.
LA Mayor Karen Bass said: "It is abhorrent that an American elected official is using human beings as pawns in his cheap political games."
Jorge Mario Cabrera, of the Coalition for Humane Immigrant Rights, said the migrants had spent 23 hours on a bus and did not get to eat or drink.
City officials said the migrants had been welcomed by agencies and charitable organisations.
In a statement on Twitter, Texas Governor Greg Abbott said: "Small Texas border towns remain overrun & overwhelmed because Biden refuses to secure the border.
"LA is a city migrants seek to go to, particularly now its leaders approved its self-declared sanctuary status."
Los Angeles city council last week passed a motion declaring itself a sanctuary city for immigrants.
The term refers to jurisdictions that limit how much they co-operate with enforcement of federal immigration law.
Governor Abbott has transported more than 20,000 migrants to other Democratic-run cities, including Washington DC, New York, Chicago, Philadelphia and Denver.
More than 5.1 million migrants have been detained after illegally crossing from Mexico into the US since Mr Biden took office, according to Customs and Border Patrol (CBP).
About 2 million of those have been released into the US.
Last month a Trump-era policy, Title 42 - which allowed for the rapid expulsion of illegal migrants - expired.
The Biden administration replaced it with new rules that deny asylum to almost all migrants who cross the US-Mexico border illegally.
While some of Mr Biden's political opponents had warned of an unmanageable influx of migrants once Title 42 lifted, the spike has so far yet to materialise.