Argentina, Brazil and Uruguay have condemned the move and recalled their ambassadors for consultations.
But Federico Franco, who replaced Fernando Lugo as president, denied that Lugo’s removal from office was a coup.
In his first news conference, Federico Franco said there had been no break with democracy.
A 39-4 vote in the Senate on Friday saw Fernando Lugo impeached, in a case stemming from his handling of clashes between farmers and police last week in which at least 17 people died.
Earlier, Argentine President Cristina Fernandez had said her country “would not validate the coup” in Paraguay.
President Cristina Fernandez also said that the South American trade bloc, Mercosur, would take “appropriate measures” at next week’s summit in Argentina.
Brazilian Foreign Minister Antonio Patriota condemned the impeachment as a “backward step” liable to be sanctioned by regional institutions such as Mercosur, Reuters news agency reports.
Federico Franco, who had been serving as Fernando Lugo’s vice-president, was sworn in as president immediately after the impeachment.
He insisted the proceedings had been conducted in line with Paraguay constitution.
“What was carried out was a political trial in accordance with the constitution and the laws,” he said.
Federico Franco acknowledged the impeachment had caused tensions with Paraguay neighbors.
“I am calm, we are going to organize the house, we are going to contact our neighboring countries in due time and I’m absolutely certain that they are going to understand the situation in Paraguay,” Federico Franco said.
The presidents of Ecuador and Venezuela, Rafael Correa and Hugo Chavez, were also outspoken in their criticism of the move.
“The Ecuadorian government will not recognize any president that isn’t Fernando Lugo,” Rafael Correa said.
“We will not lend ourselves to these tales of alleged legal formalities, which clearly attack democracy,” he added.
Venezuelan President Hugo Chavez displayed a similar sentiment: “In the name of the people of Venezuela and in the name of the Venezuelan government and as commander-in-chief, I’ll say it.
“We, the Venezuelan government, the Venezuelan state, do not recognize this illegitimate and illegal government that has been installed.”
The governments of Colombia, Mexico and Chile have said they regretted the fact that Fernando Lugo had not been “given reasonable time to prepare his defense”.
The Inter-American Commission on Human Rights said Fernando Lugo’s removal from office was an “attack on the legal foundation of the state”.
The United States and Spain have avoided publicly opposing or supporting the move, instead pressing the principle of democracy in Paraguay.
A statement from the Spanish foreign ministry said: “Spain defends full respect for democratic institutions and the state of law and trusts that Paraguay, in respect for its constitution and international commitments, will manage to handle this political crisis and safeguard the peaceful coexistence of the Paraguayan people.”
The United States took a similar stance.
US State Department spokeswoman Darla Jordan was quoted as saying: “We urge all Paraguayans to act peacefully, with calm and responsibility, in the spirit of Paraguay democratic principles.”
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