US President Barack Obama has described the removal of Honduran President Manuel Zelaya as illegal.
His remarks came after left-wing Latin American leaders declared their support for the deposed leader, who was expelled by the military on Sunday.
In Honduras, pro-Zelaya protestors have been demonstrating in the country's capital, Tegucigalpa.
Mr Zelaya's removal followed a power struggle over his plans for constitutional change.
The BBC's Stephen Gibbs in Tegucigalpa says all day hundreds of pro-Zelaya protesters have been taunting the thousands of soldiers deployed around the presidential residence, accusing them of taking part in a "criminal coup".
The ousted president, who was in office since 2006, had wanted to hold a referendum that could have led to an extension of his non-renewable four-year term in office.
Polls for the vote were due to open early on Sunday, but instead troops stormed the presidential palace at dawn, detained Mr Zelaya and flew him to Costa Rica.
The military, Congress and the Supreme Court in the Central American nation had all opposed Mr Zelaya's referendum.
We cannot allow a return to the past, we will not permit it
Our correspondent says that even though the international community regards the exiled leader as the legitimate leader of the country, any comeback will not be easy.
Speaking after a meeting with Colombian President Alvaro Uribe, Mr Obama said Mr Zelaya remained the democratically-elected leader of Honduras.
And he said a "terrible precedent" would be set if the coup were not reversed.
Earlier on Monday, speaking in Managua, the capital of Nicaragua, Venezuelan President Hugo Chavez spelled out his opposition to the situation in Honduras.
"We cannot allow a return to the past. We will not permit it," Mr Chavez said.
He spoke after talks with Mr Zelaya, President Rafael Correa of Ecuador and Nicaraguan President Daniel Ortega.
After turning up in Costa Rica on Sunday, Mr Zelaya called his ouster a plot "by a very voracious elite, an elite which wants only to keep this country [Honduras] isolated, in an extreme level of poverty".
In Tegucigalpa protestors defied a curfew order between Sunday night and Monday morning, imposed by Mr Micheletti.
As Speaker of Congress, Mr Micheletti had been the next in line to the presidency. His swearing-in was greeted with applause in Congress.
In a speech, he said that he had not assumed power under the "ignominy" of a coup d'etat.
The army had complied with the constitution, he said, and he had reached the presidency "as the result of an absolutely legal transition process".
Congress said he would serve until 27 January, when Mr Zelaya's term had been due to expire.
Presidential elections are planned for 29 November and Mr Micheletti promised these would go ahead.
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