Without directly naming Zelaya, the State Department urged citizens to "avoid actions that might provoke violence."
Zelaya, who was forced out of his country in June, is now holed up in the Brazilian embassy, surrounded by soldiers loyal to President Robert Micheletti.
"We urge that all parties refrain from actions that would lead to further unrest," State Department spokesman Ian Kelly said in a written statement Tuesday. He called for the protection of diplomatic grounds.
But in an interview with Reuters, Micheletti assured Zelaya that he can stay in Brazil's embassy for "five to 10 years" if he chooses. Micheletti said he has no intention of confronting Brazil or entering its embassy to go after Zelaya.
The State Department stressed the desire for talks, which had been moderated by Costa Rican President Oscar Arias. The dialogue stalled over Micheletti's refusal to accept a proposed power-sharing agreement.
The U.S. was quick to criticize the June 28 coup, and continues to recognize Zelaya as the president of Honduras.