However, Mariana Sanchez, Al Jazeera's correspondent in Tegucigalpa, the Honduran capital, said that the interim government had dismissed the Costa Rican statement.
"I spoke with the minister of communications a little while ago and he said it was a rumour that was being spread by the media that supports Zelaya," she said.
Honduras, a Central American country of seven million people, has been hit by protests since June 28, when Zelaya was seized by the army and forcibly deported.
Obstacles to settlement
Micheletti and Arias held separate meetings with Arias on Thursday after they refused to see each other face-to-face.
The interim leader flew back to Honduras late on Thursday, while Zelaya headed to Guatemala on Friday in an attempt to win regional support for his reinstatement as president.
"We have made the first step," Zelaya said on Friday after a final meeting with Arias.
"President Arias heard my position and that of the union and political representatives with me, which is the immediate restoration of the elected president."
But Arias said that the talks have failed to produce a clear negotiated settlement.
"I feel satisfied because a sincere, clear dialogue has been initiated, but still, the positions are very different and certainly these things ... take time, they require patience," he said.
"This could possibly take more time than imagined."
Talks to continue
Micheletti, following his return to Tegucigalpa, the capital of Honduras, said he was ready to return to talks "if necessary".
"If I am invited by President Arias, I will return with great pleasure," he said.
The US has suspended military ties with Tegucigalpa in the wake of the crisis and has said that it could cut off about $200m in aid.
The World Bank and the Inter-American Development Bank have also suspended credit to the country.
Gabriela Nunez, the finance minister in the interim government in Honduras, said on Friday that the suspension of Inter-American Development Bank and World Bank loans would cost the country $200m in 2009.
Zelaya's leftist allies in South America have also made life uncomfortable for Micheletti since the coup.
Venezuela has suspended its oil deliveries to Honduras, while Nicaragua denied Micheletti permission to fly through its airspace for the Costa Rica meeting.
Zelaya was removed from power as he was about to press ahead with a non-binding referendum on constitution change.
Congress and the courts had declared the move to hold the public vote illegal, accusing Zelaya of trying to change the charter to enable him to run for a second term in office.