(Adds Clinton, Arias quotes)

NEW YORK, Sept 21 (Reuters) - Ousted Honduran President Manuel Zelaya and the de facto government must find a way to talk and to avoid violence following his return from exile to the Central American nation, U.S. Secretary of State Hillary Clinton said on Monday.

"It's imperative that dialogue begin ... (that) there be a channel of communication between President Zelaya and the de facto regime in Honduras," Clinton said after she meet Costa Rican President Oscar Arias, who sought to broker a resolution to the crisis that followed Zelaya's June 28 ouster.

"It's also imperative that the return of President Zelaya does not lead to any conflict or violence but instead that everyone act in a peaceful way to try to find some common ground," she told reporters.

Zelaya sneaked back into Honduras on Monday almost three months after he was toppled in a coup, and took refuge in the Brazilian embassy to avoid arrest by the de facto government.

Arias has proposed that Zelaya return to office to serve out the remainder of his term, while coup participants would be given amnesty, but the de facto government has refused to consider any deal that would allow Zelaya back in power.

Arias described Zelaya's return as a moment of opportunity for the two sides to try to come to an agreement and said he was willing to go to Tegucigalpa if both sides wished.

"I would be willing to go ... if both sides, both parties asked me to," Arias told reporters. (Reporting by Arshad Mohammed, editing by Anthony Boadle)

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