Honduras' government has given Brazil 10 days to decide on the status of Manuel Zelaya, the ousted president, who took refuge in the Brazilian embassy last week after sneaking back into the country.
The interim government said in a statement on Saturday: "We urge the Brazilian government to define the status of Mr Zelaya in a period of no more than 10 days.
"If not, we will be obliged to take additional measures under international law," the statement said.
Luiz Inacio Lula da Silva, the Brazilian president, responded on Sunday by telling reporters at a summit in Venezuela that Brazil would not agree to the demands by Roberto Micheletti, Honduras' interim leader.
"Brazil will not comply with an ultimatum from a government of coup-mongers," Lula said, adding that international law protects Brazil's embassy.
Lula also demanded an apology from Micheletti.
Mariana Sanchez, Al Jazeera's correspondent in Tegucigalpa, said: "This [ultimatum] puts Brazil in a very difficult position ... because it seems that Zelaya is staging what looks like the beginning of a parallel government.
"It's difficult to see how much support [Zelaya] has. He has been here a week now, and on the first day there were a few thousand people who came to greet him. Since then, the interim government has managed to keep people out of the picture around the embassy and in the streets."
The de facto government's statement did not give details on what measures it may take if Brazil failed to meet their deadline, but said Brazil must guarantee the diplomatic mission is not used by Zelaya to "incite violence".
Since Monday, hundreds of soldiers and riot police have surrounded the embassy where protesters have held almost daily marches to demand Zelaya be reinstated.
The United Nations Security Council had condemned the purported harassment of the Brazilian embassy on Friday, after Brazilian officials complained it was "under siege".
Officials said food and supplies had only occasionally been allowed in and troops had blasted the building with high-frequency sounds.
Zelaya, a logging magnate, upset conservative elites by allying himself with Hugo Chavez, Venezuela's socialist president.
The interim government took control of Honduras after Zelaya was removed from power in late June at the height of a dispute over his plans to change the constitution.
Micheletti wants to arrest Zelaya for violating the constitution.
Zelaya demands to be restored to power, but the interim government says that elections in November will resolve the crisis.
Soldiers toppled Zelaya's government at gunpoint and sent him into exile in his pyjamas after the supreme court ordered his arrest.
His critics say his push for consitutional amendments were paving the way for a change in presidential term limits, in order to extend his rule. Zelaya denies wanting to stay in power.
His return stoked tensions in Honduras, a coffee- and textile-producing nation. One man was shot and killed in a clash between police and Zelaya supporters last week as pressure mounted to let him return to power.
The United States, the European Union and the Organisation of American States have urged dialogue to bring Zelaya back to office.
But the interim government insists that he must face justice at home.