BEIRUT, Lebanon — Two men who have reported extensively on jihadists and their activities have sued President Trump and members of his administration based on their belief that the government has put them on a “kill list” meant for terrorists, according to court documents.

Although they have worked in war zones and had contact with many members of Al Qaeda and other extremist groups, the men, Bilal Abdul Kareem and Ahmad Muaffaq Zaidan, deny that they are members of militant organizations.

In their federal lawsuit, filed on Thursday in Washington, they provide little evidence that they are on the United States kill list, which is classified, and current and former American counterterrorism officials expressed skepticism that their activities would get them marked for death by a program meant to eliminate terrorists actively plotting violence against America.

Mr. Abdul Kareem, a former standup comedian who grew up in Mount Vernon, N.Y., has been reporting from rebel-held areas in northern Syria, where he has filmed uncritical interviews with Qaeda members.