He had proposed a plan that would let Zelaya serve out the final months of his term, move up elections by one month to late October, grant a general amnesty and include representatives of the main political parties in a reconciliation government.
But Carlos Lopez, a representative of the interim government, said it was "unacceptable" for Zelaya to return to the presidency.
"My obligation in accord with the constitution and the principles of sovereign equality of states as stated in the UN charter is to tell you, Mr Mediator, in the name of a small but proud nation, I am very sorry but your proposal is unacceptable, especially in point number one," Lopez said.
"Maybe, with this effort that we have to make over the next 72 hours, we can avoid bloodshed"
Costa Rica's president
For his part, Zelaya again vowed to return to Honduras, telling reporters in the Nicaraguan capital of Managua that he would attempt to fly to Honduras at the weekend.
The Honduran military stopped Zelaya's previous attempt to return home on July 5 by blocking the runway at the airport in the capital, Tegucigalpa.
"Next weekend we will have everything necessary to make our return," Zelaya said.
"The social pact in Honduras is broken; the military broke it."
But Zelaya left "the door open for diplomacy and dialogue", particularly to Costa Rica's continued mediation efforts.
Arias has called on both sides to make an effort to find a resolution in the coming days in order to avoid violence breaking out in Honduras.
"Maybe, with this effort that we have to make over the next 72 hours, we can avoid bloodshed," he said.
"What is the alternative to dialogue? ... What happens if, tomorrow, a Honduran shoots at a soldier and then a soldier shoots his gun at an armed citizen?," he said.
Al Jazeera's Mariana Sanchez, reporting from Tegucigalpa, said it was impossible to gauge how much progress would be made over the next three days, given the differences between Zelaya's supporters and the interim government.
"It is possible that the international community, even the United States, will try to exert pressure on both sides to show some flexibility, but the problem is Zelaya's return to power," she said.
Late on Sunday, Washington urged all parties to continue the Costa Rican dialogue.
"We call on the parties to the talks to reflect upon the progress made so far, and to commit themselves to their successful conclusion," Robert Wood, acting US state department spokesman, said.
Zelaya was ousted last month and forced into exile in a military coup backed by the judiciary and congress.
The international community, particularly in the Americas, have demanded Zelaya's reinstatement but so far the interim government has refused.