The head of Venezuela’s opposition-run parliament has thrown down the gauntlet to his country’s embattled leader, Nicolás Maduro, declaring himself ready to assume the presidency, in a rare and potentially destabilizing challenge to two decades of Bolivarian rule.

Juan Guaidó told a rally in Caracas that Maduro – who began his second six-year term as president on Thursday amid a tempest of international condemnation – was an illegitimate “usurper”.

The 35-year-old politician claimed that he therefore had the constitutional right to assume leadership of the country until fresh elections were held.

“We are going to change things in Venezuela,” Guaidó told hundreds of cheering supporters in a speech he called his “declaration to the Venezuelan people”.

“We aren’t victims. We are survivors ... and we will lead this country towards the glory it deserves,” Guaidó added, calling on the people, the international community and, crucially, Venezuela’s armed forces to support him.

Guaidó, who became president of Venezuela’s national assembly last week, admitted there were no “magic solutions” to an economic crisis fuelling what the UN calls one of the greatest exoduses in Latin American history.

But he called a day of nationwide demonstrations for 23 January to intensify pressure on Maduro before concluding by shouting the rallying cry: “People of Venezuela: can we, or can’t we?” “¡Sí, se puede!” the crowd roared back. “Yes we can!”

The opposition took control of the national assembly in 2015 although it was effectively neutered by Maduro’s controversial creation of a constituent assembly in 2017 that sparked deadly protests.

People protest Nicolás Maduro’s government in Caracas, Venezuela on 11 January. Photograph: Miguel Gutiérrez/EPA

Yesiret Méndez, a 20-year-old student who was in the crowd, said she had come to hear Guaidó’s plan for the future: “And I’m ready to take to the streets again if necessary.”

Carmen de Jesús, 70, said she hoped Guaidó would be able to take control. “Maduro is usurping the power and the president of the national assembly should take over as an interim president.”

There was international support for the move too, with the head of the Organisation of American States tweeting: “We welcome the assumption of @jguaido as interim President of # Venezuela in accordance with Article 233 of the Political Constitution. You have our support, that of the international community and of the people of Venezuela # OEAconVzla.”

But there was also apprehension Guaidó’s audacious move might backfire, triggering a renewed crackdown on regime opponents.

“It’s almost certainly going to generate some sort of response from the government,” said David Smilde, a Venezuela expert from the Washington Office on Latin America advocacy group.

“They could dissolve [the national assembly] … or they could try and arrest opposition leaders or Guaidó.”

Addressing a sympathetic audience of Latin American leftists on Friday afternoon, Maduro mocked his challenger, claiming most Venezuelans did not even know who he was. “It is a show … a Hollywood-esque show,” Maduro said, adding: “The Venezuelan right is hopeless.”

Venezuela’s chavista prison minister, María Iris Varela Rangel, tweeted a more sinister message: “Guaidó, I’ve already prepared your cell and your uniform, I hope you name your cabinet quickly so I know who is going down with you.”

Smilde said Guaidó’s unexpectedly bold challenge to Maduro was a tactic the most radical members of Venezuela’s opposition had been pushing for. “But the problem with that is that they have no actual real power: they don’t control the institutions, they don’t control the guns and they don’t control the money.”

One Guaidó ally told the energy news agency Argus Media he was aware of the “life-threatening” risks of his statement: “[But] keeping silent and not invoking the constitution’s authority to strip Maduro of his executive powers would have been a surrender to the dictatorial status quo and would have buried any chance of restoring democracy for years to come.”