WASHINGTON — Both sides in Honduras’ leadership crisis Tuesday signaled their willingness to forge a diplomatic solution to the deadlock over the fate of President Manuel Zelaya, who was ousted last month in a coup.

Zelaya and interim Honduran leader Roberto Micheletti agreed to accept Costa Rican President Oscar Arias, a Nobel Peace Prize winner, as an international mediator. Arias’ appointment was backed by the United States and announced by Secretary of State Hillary Rodham Clinton after she met privately with Zelaya at the State Department.

Arias will conduct the mediation in Costa Rica, where Zelaya intends to travel from Washington. Clinton said she expected the process to begin soon.

“It is our hope that through this dialogue mechanism overseen by President Arias that there can be a restoration of democratic, constitutional order, a peaceful resolution of this matter that will enable the Honduran people to see the restoration of democracy and a more peaceful future going forward,” Clinton said.

Zelaya said he was pleased with Arias’ appointment. “I have accepted Dr. Arias’ mediation,” he told reporters after meeting with Clinton. He said the step showed that “the international community is still supporting democracy in Honduras.”

Meanwhile, in Honduras, Micheletti, who had vowed not to negotiate until “things return to normal,” appeared to open some space for a settlement to the crisis that began June 28 when Zelaya was detained by the military and forced into exile.

Arias “is a man with a lot of credibility in the world,” Micheletti told HRN radio. “We are open to dialogue. We want to be heard.”

The interim leader said he would send a delegation soon to Costa Rica, although he stressed that the meeting “doesn’t mean that Zelaya will be allowed to return.” Still, his tone was less belligerent than in recent days, when officials promised to arrest Zelaya on charges including treason as soon as he sets foot on Honduran soil.

Micheletti did not repeat his earlier insistence that Zelaya’s return is not negotiable, though he did say that Zelaya broke the law. The new government has threatened to arrest Zelaya for 18 alleged criminal acts, including treason and failing to implement more than 80 laws approved by Honduran lawmakers since he took office in 2006.

Arias won the Nobel Peace Prize in 1987 for helping broker an end to Central America’s civil wars.

“He is the natural person to assume this role,” Clinton told reporters, adding that while the Obama administration continues to support efforts by the Organization of American States to resolve the crisis, she felt that it was necessary to name a specific mediator.