Major regional players Brazil, Colombia, Chile, Peru and Argentina all gave their backing to Juan Guaido's self-proclamation as Venezuela's acting president, which he made in front of crowd of tens of thousands of supporters in Caracas.
Mexico, however, stood apart, saying it recognizes "the authorities elected in accordance with the Venezuelan constitution," seen as a lukewarm nod to Maduro.
The avalanche of support for Guaido dramatically raised the stakes in Venezuela, an oil-rich nation has become deeply impoverished under Maduro.
Maduro has clung to power through the support of the Venezuelan military, and he is an ally of Russia, which last month sent two nuclear-capable bombers to the country to participate in a military drill.
The United States said Wednesday it stood ready to use "all options" if Maduro tries to quash the opposition, in what was an implied threat of military force.
President Donald Trump said Guaido's National Assembly was "the only legitimate branch of government duly elected by the Venezuelan people."
Maduro responded by saying he was cutting off diplomatic ties with the United States, as his riot police clashed with opposition supporters in Caracas.
"Get Out! Leave Venezuela. Here we have dignity, damn it," Maduro said, giving US diplomats 72 hours to depart.
But Guaido tweeted in response a statement that, under him, Venezuela wants countries "to maintain their diplomatic presence in our country."
Tweeting from the Swiss ski resort of Davos, where he and other leaders were attending the World Economic Forum, Brazilian President Jair Bolsonaro said: "Brazil recognizes Mr Juan Guaido as Venezuela's interim president."
He added that "Brazil will support politically and economically the process of transition so that democracy and social peace return to Venezuela."
Bolsonaro, a far-right former paratrooper who has set about forging close ties with Trump's administration since taking power at the beginning of January, has repeatedly vowed to challenge Maduro in any way he can.
He initially said he was open to discussing Brazil hosting a US military base, before changing his mind when the idea sparked objections from his military brass.
Colombian President Ivan Duque, another US ally also at Davos, told reporters his country was behind Guaido and will "accompany this process of transition to democracy so that the Venezuelan people free themselves of their dictatorship."
Canadian Foreign Minister Chrystia Freeland expressed her country's "full support" for Guaido, adding: "It's an important day for Venezuela and I'm grateful for the solidarity of the Lima Group in speaking out on this."
Eleven members of the 14-nation Lima Group -- Argentina, Brazil, Canada, Chile, Colombia, Costa Rica, Guatemala, Honduras, Panama, Paraguay and Peru -- later issued a joint statement endorsing Guaido as interim president.
The three holdouts included Mexico, which has maintained a principle of non-intervention under leftist President Andres Manuel Lopez Obrador, as well as Guyana and Santa Lucia.
Lopez Obrador's spokesman said on Twitter that while Mexico "for the moment" was not changing its relations with Caracas, it was "analyzing the situation in Venezuela."
The United States is not a member but supports the group, which has taken an increasingly strident stance against Maduro, whom it sees as anti-democratic.
The European Union did not join the countries lining up behind Guaido, but EU Council President Donald Tusk tweeted that "I hope that all of Europe will united in support of democratic forces in Venezuela."
Tusk added: "Unlike Maduro, the parliamentary assembly, including Juan Guaido have a democratic mandate from Venezuelan citizens."