Texas Governor Gregg Abbott and Florida Governor Ron DeSantis, long opposed to President Joe Biden's border policies, this week transported dozens of migrants to northern US cities.
On Thursday Mr Abbott claimed that he had sent two busloads of migrants to be dropped off near the private residence of Vice President Kamala Harris at the Naval Observatory in north-west Washington.
Migrants who were dropped off outside Ms Harris's home on Thursday morning were fleeing violence and repressive regimes in Venezuela, Nicaragua and Cuba.
“These were children. They were mums. They were fleeing communism,” White House spokeswoman Karine Jean-Pierre told reporters on Friday.
Condemning the moves by Mr Abbott and Mr DeSantis, she said migrants were being used “as political pawns … like chattel in a cruel, premeditated political stunt”.
Ms Jean-Pierre noted that the roughly 50 Venezuelan migrants sent by Mr DeSantis to the wealthy enclave of Martha's Vineyard had reportedly been misled about their destination.
“These are the kinds of tactics we see from smugglers in places like Mexico and Guatemala,” she said.
Speaking at the Congressional Hispanic Caucus Institute Gala in Washington on Thursday night, Mr Biden accused Republicans of playing politics instead of engaging in bipartisan solutions to the country's immigration problem.
“What they’re doing is simply wrong,” he said. “It’s un-American. It’s reckless.”
The border state governors have sent thousands of migrants to Democratic cities as a sign of their opposition to the Biden administration's border policies.
The White House has denied claims from Republican leaders that its policies encourage migrants to cross into the US. Migration is brought about by other factors, such as violence and poor economic conditions in Central and South America, the White House says.
Mr Biden said the US has a process in place to manage migrants crossing from the US-Mexico border.
“Republican officials should not interfere with that process by waging … these political stunts,” he said.
These and other migrants cannot be expelled from the country as many entered the US to request asylum or because Mexico will not accept them if there is an attempt to push them back across the border.
After migrants seeking asylum cross the southern border, they wait in a Customs and Border Protection facility until they are released into the US to wait for their cases to be reviewed.
Democrats have argued that a policy instituted under former president Donald Trump that sent migrants back to Mexico while they waited for their asylum cases to be reviewed was inhumane.
On Wednesday, two planes sent from Florida carried migrants to the wealthy enclave of Martha's Vineyard in Massachusetts without providing advanced notice.
Mr DeSantis, who is seeking re-election this year and is a possible 2024 presidential candidate, said Mr Biden has “refused to lift a finger” to secure the border.
Massachusetts Governor Charlie Baker announced on Friday that a new temporary shelter will be established at Joint Base Cape Cod as Martha's Vineyard does not have the resources to sustain its humanitarian efforts.
Mr Baker said 125 members of the state's National Guard would be activated as part of the effort.
Agencies contributed to this report