"I kind of feel like Clint Eastwood. Go ahead, Mayor. Make my day," said Abbott on Fox News Wednesday morning.
Gov. Abbott and Adams have gone back and forth since Texas began busing migrants from the Texas-Mexico border to the Big Apple.
On Wednesday, three more buses carrying nearly 100 migrants from the Lone Star State arrived in New York.
"There are children amongst them. There are families. They need to be treated humanely. That's all we're asking for. Don't treat them like political pawns," said Manuel Castro, the commissioner of the NYC Mayor's Officer of Immigrant Affairs.
Texas has sent more than 5,000 asylum seekers to New York and Washington, D.C. to bring awareness to what Gov. Abbott calls the illegal immigration crisis that border states are facing.
The mayors in both cities have asked for federal assistance to deal with the migrants.
Abbott says he will continue to bus migrants who crossed illegally into New York, Washington, and possibly other communities.