Gleisi Hoffmann adds to divisions in Brazil's opposition in confronting new, far-right President Jair Bolsonaro. Bolsonaro calls him a dictator.
Anti-government politicians successfully rallied thousands to the streets across Venezuela for four months of demonstrations in 2017, when clashes with government forces left more than 120 protesters dead and thousands injured.
The US and 13 other countries in the Americas said last week that they would not recognise Mr Maduro's presidency. Writer Marcelo Rubens Paiva called it "a monstrous stupidity".
President Mauricio Macri made his opinion clear via Twitter: "Nicolas Maduro today is making a mockery of democracy".
The announcement came nearly immediately after Maduro took the oath of office in Caracas.
Minutes after Mr Maduro was sworn in, Paraguayan President Mario Abdo tweeted that he was cutting diplomatic ties with Venezuela and was immediately withdrawing his country's diplomats from Caracas.More news: Chris Jericho On Why He Really Signed With All Elite Wrestling
The US Embassy in Trinidad and Tobago issued a statement on Thursday condemning Venezuelan President Nicolas Maduro's illegitimate usurpation of power following what it deemed the unfree and unfair elections imposed on the Venezuelan people on May 20.
Venezuela's Ambassador Samuel Moncada called the measure adopted Thursday "a hostile act. against the will of our nation".
The resolution was approved with 19 votes in favour, six against, eight abstentions and one absent.
Despite his typically grandiose rhetoric, the inauguration has created more problems for the Maduro regime than solutions, as scores of countries came together to denounce his attacks on democracy and illegitimate rule.
Maduro's second term extends Venezuela's socialist revolution amid widespread complaints that he has stripped Venezuela of its last vestiges of democracy.
Thursday's swearing-in comes amid widespread global condemnation over allegations that his election was undemocratic.More news: The Accidental Prime Minister: Delhi HC dismisses PIL against trailer ban
Maduro rejected the accusation, vowing to continue the legacy of the late President Hugo Chavez and accused the United States of trying to ignite unrest through its increasing economic sanctions.
The political opposition is severely constrained as Maduro continues to enjoy the support of the military.
Members of the so-called Group of Lima, which includes Brazil, Argentina and Colombia, said Maduro's new term would be illegitimate because the 2018 election that gave him a second term was not free or fair and that they would not recognize his leadership.
But Cuba's President Miguel Diaz-Canel, Bolivian President Evo Morales and President Anatoli Bibilov of a breakaway province of Georgia were among the foreign leaders who attended the ceremony at the country's Supreme Court. Canada has provided $2.2-million in humanitarian assistance to Venezuela and is a member of the Lima Group of countries that is trying to bring worldwide pressure to bear on the South American country. But there will be some long-time friends in attendance both from overseas and at home.
Maduro's popularity has plunged amid scarcities, hyperinflation and rising authoritarianism that have sparked a mass emigration.More news: BSPD welcomes children’s oral health reference in NHS Long Term Plan