Mr Guaidó declared himself "acting president" on Wednesday
Tens of thousands of Venezuelans are taking to the streets in protest against President Nicolás Maduro.
Mr Guaidó, who called for the demonstrations, declared himself acting leader in Caracas on Wednesday.
Mr Maduro was sworn in for a second term earlier this month, amid widespread allegations of vote-rigging.
Early images from Wednesday's protests showed some demonstrators facing off against National Guard security forces in the capital.
Mr Guaidó, who is head of the country's National Assembly, has called on armed forces to disobey the government.
Activist groups said earlier that at least four people were killed overnight ahead of the demonstrations.
There are reports of tens of thousands of people out on streets across the country - including some counter-demonstrations being held in support of Mr Maduro.
In a statement on Wednesday, President Trump urged other governments to follow his lead in recognising Mr Guaidó.
He described Mr Maduro's leadership as "illegitimate" and said the country's congress, led by Mr Guaidó, was the "legitimate branch of government" in the country.
"The people of Venezuela have courageously spoken out against Maduro and his regime and demanded freedom and the rule of law," his statement said.