SAN JOSE, Costa Rica,  (Reuters) – The two rivals for  power in Honduras started a dialogue through a mediator yesterday, but there was no face-to-face meeting or breakthrough  to solve the political crisis sparked by last month’s coup.

Ousted Honduran President Manuel Zelaya, and the politician  who replaced him after the June 28 coup, Roberto Micheletti,  left behind delegations in Costa Rica’s capital San Jose,  holding talks under the mediation of Costa Rican President  Oscar Arias.

Both men met separately with Arias, a Nobel Peace Prize  winner, but they did not sit down for direct discussions.  “There was no face-to-face meeting,” Costa Rican presidential  spokesman Pablo Gueren told reporters.

The absence of a direct meeting or any public sign of  reconciliation suggested Arias faced a tough task in trying to  bring together the entrenched positions held by the rivals over  the coup, which has stirred up tensions in Central America.

“The dialogue has started,” Micheletti, who was installed  by Honduras’ Congress after Zelaya’s overthrow, said before  flying back to his country, a coffee and textile exporter which  is one of the poorest in the Americas.

The United States and the Organization of American States  are pressing for Zelaya’s peaceful reinstatement, which OAS  chief Jose Miguel Insulza said was the key for a successful  outcome to the talks in San Jose.

But although Micheletti said his interim government would  go ahead with previously scheduled elections in November, he  showed no indication of being ready to give up power despite  international pressure and repeated demands from Zelaya.

Costa Rica’s Communications Minister Mayi Antillon said the  two delegations would try to move toward an agreement “and  hopefully … the presidents will come back”.

“There are respectful talks around a table,” she added.

Micheletti said any solution would have to respect  Honduras’ laws and constitution.

Reflecting the distance between the two sides, Micheletti  has insisted Zelaya’s ouster was lawful because he violated the  constitution by seeking to lift presidential term limits.

Zelaya stressed that both the OAS and the United Nations  General Assembly backed his reinstatement. He has called  Micheletti a “criminal” and said he was guilty of treason.