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United States President Donald Trump formally recognised Guaido shortly after his announcement and praised his plan to hold elections. That was swiftly followed by similar statements from Canada and a slew of right-leaning Latin American governments, including Venezuela's neighbours Brazil and Colombia.
At a rally in the east of the capital Caracas that drew hundreds of thousands of Venezuelans, Guaido accused Maduro of usurping power. He promised to create a transitional government that would help the country escape its hyperinflationary economic collapse.
"I swear to assume all the powers of the presidency to secure an end to the usurpation," 35-year old Guaido, the head of the opposition-run congress, told an exuberant crowd.
Guaido's declaration takes Venezuela into uncharted territory, with the possibility of the opposition now running a parallel government recognized abroad as legitimate but without control over state functions.
In a televised broadcast from the presidential palace, Maduro accused the opposition of seeking to stage a coup with the support of the United States, which he said was seeking to govern Venezuela from Washington.
"We've had enough interventionism, here we have dignity, damn it! Here is a people willing to defend this land," said Maduro, flanked by top Socialist Party leaders.
Any change of government will rest on a shift in allegiance within the armed forces. So far, they have stood by Maduro through two waves of street protests and a steady dismantling of democratic institutions.
US Secretary of State Mike Pompeo called on the Venezuelan military to protect "the welfare and well-being of all Venezuelan citizens," along with US citizens in Venezuela. Pompeo said the United States would take "appropriate actions" against anyone who endangered the safety of US personnel.
The United States would conduct its diplomatic relations with Venezuela through "the government of interim President Guaido," he said.
Defense Minister Vladimir Padrino said on Wednesday that the armed forces did not recognize a self-proclaimed president "imposed by shadowy interests ... outside the law." Military top brass indicated their continued support for Maduro in tweets.
In a potent symbol of Venezuelan anger, demonstrators in the southern city of Puerto Ordaz on Tuesday toppled a statue of late socialist leader Hugo Chavez. They broke the statue in half and dangled part of it from a bridge.
Maduro took power in 2013 after his mentor Chavez died. As the oil price sank and revenues dried up, the social welfare programs designed by Chavez faltered. Venezuela spiraled into its worst-ever economic crisis, with hyperinflation forecast to reach 10 million percent this year.
But Maduro nevertheless started a second term on Jan. 10, following a widely-boycotted election last year that many foreign governments described as a sham.
In the Chacao district of eastern Caracas, a traditional opposition bastion, a dozen protesters spoke of a renewed confidence in dislodging Maduro and predicted a new wave of demonstrations.
Many said they had protested in previous years but had lost hope as Maduro tightened his grip on power. Some 3 million Venezuelans have fled abroad over the past five years to escape widespread shortages of food and medicine.
"The struggle will be long," said Ciro Cirino on Altamira plaza, minutes after police on motorbikes charged a crowd of several thousand protesters, firing tear gas to disperse them.
"The police push us back - once, twice, three times - and we keep going back. We are going to be here until there is a change," said Cirino, a 35-year-old computer programmer.
Venezuela's constitution says if the presidency is determined to be vacant, new elections should be called in 30 days and that the head of the congress should assume the presidency in the meantime.
However, the pro-government Supreme Court has ruled that all actions taken by the National Assembly congress are null and void and the government has jailed dozens of opposition leaders and activists for seeking to overthrow Maduro through violent street demonstrations in 2014 and 2017.
As pressure mounts on Maduro both internally and externally, the Trump administration is considering sanctions on Venezuelan oil as soon as this week, according to sources.
The South American OPEC country has the largest crude reserves in the world and is a major supplier to US refiners, though output is hovering near 70-year lows and reaction in the oil markets was muted on Wednesday.
Local bonds rebounded, with Venezuela's benchmark 2027 bond trading above 31 cents on the dollar for the first time since May 2018.
Eight people have so far died across Venezuela in clashes with police this week and authorities have arrested 59 people since Monday, according to local officials and rights groups.
On Caracas' streets on Wednesday, protesters wielding rocks and clubs clashed with police, according to Reuters witnesses.
"We're hungry. Look how skinny I am: there's no food in my house," said one young man in Chacao, holding a molotov cocktail. He declined to give his name. "We have to get rid of Maduro."