Senator John Thune, a senior Republican from South Dakota, told reporters lawmakers are "trying to work out ... what would be effective in terms of slowing this."
The U.S. Commerce Department oversees the Internet's management largely because it was invented in the United States.
Some Republican politicians, including Senator Ted Cruz of Texas, want to block the handover to global stakeholders, such as businesses, tech experts and public interest advocates.
Opponents of the transition said it could stifle online freedom by giving voting rights to authoritarian governments.