Update 8.24am: Donald Trump has rejected a request from the Venezuelan president to speak with him on the phone.
Previously the U.S. president admitted he wouldn't rule out military action in response to the country's political chaos.
The White House says Mr Trump will take the request as soon as "democracy is restored" in Venezuela.
Earlier: US president Donald Trump has stepped up the rhetoric against Venezuela, saying he had not ruled out military action against the crisis-hit Latin American state.
Speaking to reporters at his Bedminster, New Jersey, golf club, Mr Trump bemoaned the country's growing humanitarian crisis and declared that all options remain on the table - including a potential military intervention.
"We have many options for Venezuela and by the way, I'm not going to rule out a military option," he volunteered, adding: "A military operation and military option is certainly something that we could pursue."
Venezuela's defence minister hit back, calling Mr Trump's talk of a military intervention an act of "craziness" and "supreme extremism".
General Vladimir Padrino said: "With this extremist elite that's in charge in the US, who knows what will happen to the world?"
On Thursday, Mr Trump said he discussed Venezuela along with North Korea and Afghanistan in a security briefing with top national security aides and his vice president Mike Pence.
Mr Pence is travelling to Colombia on Sunday to begin a regional trip that is expected to include discussions on how to deal with the Venezuela's socialist president Nicolas Maduro for allegedly trampling his country's constitutional order in a power grab.
Mr Maduro has tried to deflect the pressure from Washington and on Thursday he said he wanted to meet Mr Trump, perhaps next month at the United Nations General Assembly in New York.
"Mr Donald Trump, here is my hand," the president told delegates at the constitutional assembly, adding that he wanted as strong a relationship with the US as he had with Russia.
But late on Friday the White House rejected the request to meet Mr Trump.
A statement by the White House press secretary said the president "will gladly speak with the leader of Venezuela as soon as democracy is restored in that country".
"Trump has asked that Maduro respect Venezuela's constitution, hold free and fair elections, release political prisoners, cease all human rights violations, and stop oppressing Venezuela's great people. ... Instead Maduro has chosen the path of dictatorship," the statement said.
The Trump administration has imposed sanctions on Mr Maduro and more than two dozen other former and current Venezuelan officials.
Reaction in Latin America has been far more subdued, reflecting long-held reluctance by much of the region to encroach on a neighbour's sovereignty and some lingering ideological affinity for the anti-imperialist revolution started by the late president Hugo Chavez.
Several attempts to punish Venezuela at the Organisation of American States have failed due to a lack of consensus.
Meanwhile Peru expelled Venezuela's ambassador as regional pressure built on Mr Maduro's government.
The Venezuelan government retaliated by ordering the head of Peru's embassy in Caracas to leave and called Peruvian president Pedro Pablo Kuczynski an "enemy" of Venezuela and of Latin American unity.
Peru gave ambassador Diego Molero, a former Venezuelan defence minister, five days to leave the country.
As part of what it said was a firm commitment "to help restore Venezuela's democracy", Peru's administration also refused to accept a diplomatic protest made by Mr Maduro over Peru's hosting this week of foreign ministers from 17 regional nations who refused to recognise the new, loyalist-packed special assembly that is to rewrite the constitution.
The action by Peru, the strongest yet from a Latin American government, came as the Trump administration considered putting economic sanctions on Venezuela to punish Mr Maduro for what Washington calls his illegitimate power grab.
A few hours later, Venezuela's foreign ministry announced that it was giving Peru's top envoy in Caracas, Carlos Rossi, five days to leave the country.
Peru's president has until recently been a lonely exception among Latin American leaders in openly condemning Mr Maduro.
Mr Kuczynski, a former Wall Street investment banker who spent decades living in the US, is frequently mocked on Venezuelan state TV and was once referred to as the "empire's lapdog" by an official.
Mr Maduro's government has sent mixed signals about how much more confrontation it is willing to accept.
This week, the government-packed Supreme Court ordered the arrest of two Caracas-area mayors for protecting protesters in their districts.
And on Friday, Tarek William Saab, installed as chief prosecutor after the constitutional assembly ousted his outspoken predecessor, warned that he would reopen investigations against protesters for the use of violence and even destruction of trees used to build barricades at demonstrations.
At the same time, the constitutional assembly said on Friday it would debate a proposal to push up to October elections for governors in all of Venezuela's states.
It is a possible sign that the government is looking to negotiate a deal with the opposition, although many question if the constitutional assembly, which has a free hand to upend institutions, will even allow elections that were originally slated to take place last year will be allowed to go forward.