Senator John Cornyn, a Texas Republican, said on Thursday that the F.B.I. had agreed to his request to help track down dozens of Democratic Texas state lawmakers who left the state to prevent a vote on a redistricting plan.

The activation of federal agents could create a standoff between the Trump administration and state leaders in Illinois, where some of the absent Democrats have taken refuge.

It was not clear on Thursday morning whether federal agents had taken any action yet in the case, or what role they might eventually play.

The whereabouts of the Texas lawmakers are widely known, but until now at least, they had considered themselves safe from arrest because they were far from the jurisdiction of Texas law enforcement agencies.

“I am proud to announce that Director Kash Patel has approved my request for the F.B.I. to assist state and local law enforcement in locating runaway Texas House Democrats,” Mr. Cornyn said in a statement. “I thank President Trump and Director Patel for supporting and swiftly acting on my call for the federal government to hold these supposed lawmakers accountable.”

This is a developing story. Check back for updates.