Manuel Zelaya (left) called for his immediate restoration as president
Interim Honduran leader Roberto Micheletti has left talks in Costa Rica without meeting ousted President Manuel Zelaya, who was forced out last month.
Mr Micheletti said officials would continue talks with the mediator, Costa Rican President Oscar Arias.
Mr Zelaya and Mr Micheletti held separate meetings with Mr Arias, but there was scant sign of a breakthrough.
Each Honduran had made it a condition of attending talks that he would not have to meet the other, officials said.
The Costa Rican president had been hoping to bring the former political allies together for their first direct meeting since the bloodless ousting of Mr Zelaya, but neither would budge.
"We have no illusions, this may take longer than what was imagined," said Mr Arias, who won the 1987 Nobel Peace Prize for helping resolve Central American civil wars.
28 June: Troops expel Zelaya; Micheletti becomes interim leader
29 June: US President Obama condemns the overthrow as illegal
4 July: Organization of American States suspends Honduras
5 July: Zelaya's jet is turned back from Honduras, amid clashes
9 July: Micheletti leaves mediated talks in Costa Rica
Mr Micheletti, who insists Mr Zelaya should give up claims to the presidency, said he was returning to Honduras "totally satisfied".
In the Costa Rican capital, San Jose, Mr Zelaya said he had told Mr Arias his position was still for "the immediate restoration of the elected president [himself]".
The talks were expected to continue on Friday, despite the absence of Mr Micheletti, who is former speaker of the Honduran parliament.
Mr Zelaya had earlier described Mr Micheletti as a "criminal" and said he expected the leaders of the coup to leave power in 24 hours.
The BBC's Steven Gibbs in the region says the two sides did agree that they both respect the Honduran constitution.
But, he adds, that means little, as interpretation of the charter has divided the rivals since this crisis began.
The interim government has said Mr Zelaya should face trial in Honduras for allegedly abusing the constitution.
On arriving back in the Honduran capital, Tegucigalpa, Mr Micheletti said: "We are in agreement with his [Mr Zelaya's] return here - but to be sent directly to the courts."
In Honduras itself, thousands of pro- and anti-Zelaya protesters took to the streets on Thursday.
Supporters of the ousted leader cut off several highways, while Mr Micheletti's backers took to the streets of San Pedro Sula and other towns.
Mr Zelaya was forced out of Honduras at gunpoint on 28 June.
The political crisis erupted after he attempted to hold a non-binding public consultation to ask people whether they supported moves to change the constitution.
Opponents said that could have led to the removal of the current one-term limit on serving as president and so paved the way for Mr Zelaya's possible re-election.