US Secretary of State Mike Pompeo says his country will take additional measures in support of Venezuela's opposition leader Juan Guaidó.
Mr Pompeo called on other countries to co-operate in efforts to remove President Nicolás Maduro from office.
Mr Guaidó travelled to Colombia to meet Mr Pompeo on the sidelines of a regional conference.
This is the second time he has defied a travel ban imposed by Venezuela's pro-government Supreme Court.
Mr Maduro and Mr Guaidó have been at loggerheads for more than a year, after Mr Guaidó - who heads the National Assembly - declared himself interim president, claiming Mr Maduro's re-election in 2018 was fraudulent.
Despite international pressure and US sanctions on the crucial oil sector, Mr Maduro has managed to stay in power, supported by Russia, Cuba and a handful of other countries as well as the powerful Venezuelan military.
"I would fully expect there will be further action that the United States would take to continue to support President Guaidó and the Venezuelan people," Mr Pompeo told journalists.
He referred to Mr Guaidó as president as the US and more than 50 other nations have recognised him as the legitimate leader.
"We do not talk about particular sanctions, but everyone can fully expect that the United States is not done," Mr Pompeo said.
"The world must continue to support the Venezuelan people's effort to restore their democracy and put an end to Maduro's tyranny which harms millions of Venezuelans and has an impact on Colombia and indeed on the entire region."
Mr Guaidó was attending a counter-terrorism conference in the Colombian capital, Bogotá, along with foreign ministers from several Latin American nations.
He said he would next travel to Davos in Switzerland to attend the World Economic Forum.
Mr Maduro accuses the US of orchestrating a coup to oust him. But in an interview he seemed to open the door for direct talks with the US.
Speaking to the Washington Post, Mr Maduro said: "If there's respect between governments, no matter how big the US is, and if there's a dialogue, an exchange of truthful information, then be sure we can create a new type of relationship."
Mr Guaidó was received by Colombian President Iván Duque with full presidential honours.
President Duque said they had discussed the importance of re-establishing democracy in Venezuela as well as measures to help those fleeing Venezuela's crippling economic and political crisis.
According to United Nations figures, 4.8 million Venezuelans have left their country since 2016, with 1.6 million arriving in neighbouring Colombia.
Almost a quarter of Venezuela's 30 million people are in need of aid, the UN says.
Barred from travelling
It was not clear how Mr Guaidó reached Colombia. He had not left Venezuela since last February, when he first defied the travel ban to drum up support for the opposition.
The rivalry between Mr Guaidó and Mr Maduro has flared in recent weeks as Mr Guaidó stood for re-election as National Assembly Speaker, the position on which his claim to the post of acting president rests.
He was prevented by the National Guard from entering the National Assembly building, forcing him to move the session to another location where about 100 lawmakers re-elected him.
The scenes of Mr Guaidó trying to clamber over the railing surrounding the National Assembly and being pushed back by the National Guard were widely condemned, even by countries such as Mexico which had so far not backed the opposition leader.