"We will continue busing migrants until Biden secures the border," Abbott said via Twitter.
Abbott emphasized that mayors of so-called "sanctuary cities" in the United States are complaining they are overwhelmed by several dozen migrants arriving on buses from Texas, but they are only a fraction of what Texas faces on a daily basis.
Earlier on Wednesday, the governor of the state of Illinois Governor J.B. Pritzker issued a disaster proclamation on Wednesday to enhance efforts to adequately respond to the hundreds of undocumented migrants arriving to Chicago from Texas.
Washington Mayor Muriel Bowser last week declared a public emergency in the city due to the arrival of thousands of undocumented migrants bused to the area from Texas and Arizona.
On Friday, Abbott said Texas has transported some 10,000 undocumented migrants who crossed illegally into the United States to sanctuary cities like Washington, New York and Chicago.
Well over two million migrants have entered the United States illegally via the US southern border since October, breaking last year's record set under the Biden administration's watch. The influx has severely strained local, state and federal resources on the southern border that are trying to handle the situation.