The US has urged ousted Honduran President Manuel Zelaya to negotiate rather than try to force his way back into power.
After meeting Mr Zelaya, US Secretary of State Hillary Clinton said he had agreed to a new mediation effort that is to be led by Costa Rican President Oscar Arias.
The offer of mediation has already been accepted by Honduras' interim president Roberto Micheletti.
Mrs Clinton also made clear the US does not want Mr Zelaya, who was toppled in a 28 June coup, to try again to return to Honduras.
Mr Zelaya tried to fly home on Sunday, but the interim government stopped his plane from landing.
At least one person was killed when troops clashed with pro-Zelaya protesters who went to the airport in the capital, Tegucigalpa, to meet him.
'I believe it is a better route for him to follow at this time than to attempt to return in the face of the implacable opposition of the de facto regime,' Mrs Clinton said.
'So, instead of another confrontation that might result in a loss of life, let's try the dialogue process and see where that leads, and let the parties determine all the various issues as they should,' she added.
Ms Clinton added her voice to a call for a return to constitutional and democratic order in Honduras.
However, she did not explicitly call for Mr Zelaya to return to power, saying that this should be negotiated by the parties themselves.
Mr Micheletti said: 'We've accepted him as the mediator, given the high profile that the president of Costa Rica has.'
But he added: 'We maintain our position that President Zelaya should not return. He committed crimes and he must pay for them.'