"We have many options for Venezuela including a possible military option if necessary", Trump told reporters.
Addressing the newly elected all-powerful Constituent Assembly Thursday, Maduro instructed Venezuela's foreign minister to arrange a meeting or telephone conversation with US President Donald Trump.
The White House later said that Mr Maduro had requested a phone call with the American president.
Saturday's statement by the Foreign Ministry reiterated concerns about a "breakdown in the democratic order" in Venezuela and called for the United Nations secretary-general to help negotiate a solution. After his trip to Colombia, Pence will travel to Argentina, Chile and Panama, representing the highest level tour of the Trump administration to the region.
Trump did not specify what type of options he had in mind.
"We have many options for Venezuela and by the way, I'm not going to rule out a military option", Trump volunteered, adding that "a military operation and military option is certainly something that we could pursue". Citing the resentment stirred in Latin America by the long US history of military interventions in the region, General H.R. McMaster said recently that he didn't want to give Maduro any ammunition to blame the "Yankees" for the "tragedy" that has befallen the oil-rich nation.
"Some of these countries have recently taken positions absolutely contrary to our sovereignty and independence but still have rejected the declarations of the USA president".
Trump has explained that he takes these meetings in the name of diplomacy, arguing that it is best to at least have a dialogue open even with those who may be your opposition. Mexico and Colombia joined in with statements of their own.
Venezuela is retaliating in kind for Peru's expulsion of its ambassador.
"All foreign or domestic threats to resort to force undermine the goal of reinstating democratic governance in Venezuela, as well as the principles enshrined in the United Nations charter", said Peru's Foreign Minister Ricardo Luna.
President Juan Manuel Santos has called his Venezuelan counterpart Nicolas Maduro a dictator and held out the possibility of breaking off diplomatic relations if Maduro doesn't reverse course on measures seen as increasingly authoritarian.
The new legislative superbody, which made waves last weekend by firing a dissident chief prosecutor, took new action on Saturday on the country's election timetable. However, the opposition leaders describe the situation as a power grab.
The assault highlighted the growing volatility in the oil-rich but economically-ailing country after four months of sustained anti-government protests and unrest in which more than 120 people have been killed.
The National Electoral Council (CNE) was asked by the assembly to set the exact date for the governors' election.
The attack dramatically ratcheted up tensions in Venezuela's long-running crisis, raising the prospect it could spill into some form of armed conflict.