Trump issued an executive order in June to force the Hague-based tribunal out of the investigation into potential war crimes by US military and intelligence officials in Afghanistan.
It threatened “serious consequences” for anyone giving support to the work of the ICC.
The executive order was followed last month by the imposition of sanctions against the ICC chief prosecutor, Fatou Bensouda, and another senior ICC official.
The lawsuit, which was filed on Wednesday morning in a federal court in New York, calls for the enforcement of Trump’s “outrageous” order to be halted while the court considers its constitutionality.
The lawyers now say they have had to cancel speeches and presentations, end research, abandon writing ICC-related articles and dispensing advice and assistance to victims of atrocities.
“This is just a wallop, a gut punch, silencing the activities that really have been my life’s work,” said one of the plaintiffs, Diane Marie Amann, professor of international law at the University of Georgia.
“I work on behalf of children who are affected by armed conflict, who are killed, tortured, sexually abused, forced to become child soldiers, and trafficked,” Amann said.