Venezuela is now going through a political crisis, and the country's president, Nicolas Maduro, has repeatedly accused Washington of orchestrating a state coup in Venezuela. They say Maduro was elected through fraud.
Mr Pompeo said later he would not speculate on what happens next.
Maduro has received support from Russia, Syria, Turkey and China as well as longtime allies Cuba and Bolivia.
Maduro accused Washington of orchestrating a coup in the Latin American country and said that Caracas was severing diplomatic ties with Washington. Reuters reported on Friday that private military contractors who do secret missions for Russian Federation flew into Venezuela to beef up security for Maduro.
Guaido's goal as he tries to consolidate his parallel government, which has worldwide support but no control of the state, is to win over defectors by promising an amnesty policy that would let soldiers, police and civilians take part in public life after a transition, without punishment.
On Saturday, Britain, Germany, France, and Spain said they would recognize Guaido as Venezuela's leader if Maduro fails to call fresh elections in eight days, an ultimatum the Venezuelan foreign minister called "childlike".
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The United States has condemned last year's Venezuelan election, in which Maduro won another term, as a charade that was neither free or fair.
The Trump administration and several other nations took steps to recognize opposition leader Juan Guaido as Venezuela's interim president, which Maduro called an attempted coup.
Maduro gave USA diplomats 72 hours to leave the country, but the Trump administration said it wouldn't comply, arguing that Maduro is no longer Venezuela's legitimate president.
The United States on Saturday, January 26, pressed all nations to "stand with the forces of freedom" in Venezuela, encouraged by a tougher European line on Maduro.
The fact that Maduro blinked and opened a thirty-day window for negotiations is a positive sign, but it seems unlikely in the extreme that either side will back down at this point. "I sent many messages to Donald Trump", he said.
"I order you not to shoot", he said. This is the USA supporting the people of Venezuela, who want their constitution and democracy followed.
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Maduro, who so far appears to have the backing of the decisive military, has dug in, accusing the US of orchestrating a coup by encouraging Guaido to declare himself interim president and then leading a chorus of nations that immediately recognized his rule.
Each man appeared ready to defend his claim to the presidency no matter the cost, with Guaido telling supporters that if he is arrested they should "stay the course" and peacefully protest.
Vice president Mike Pompeo urged all nations to end Venezuela's "nightmare" and support Mr Guaidó in a United Nations debate. The former union leader cruised to victory after blocking main opposition candidates from running.
Meanwhile, Venezuela defused a diplomatic conflict with the United States, suspending a demand that USA diplomats leave the country within 72 hours.
But Pompeo warned Maduro not to "test the United States on our resolve to protect our people".
Pompeo was accompanied to NY by Elliott Abrams, who was named a day earlier as the US special representative for Venezuela. That set the stage for a showdown at the hilltop U.S. Embassy compound Saturday night, when the deadline was to expire.
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Last night was supposed to be the deadline for American diplomats in Venezuela to vacate the country as ordered by dictator Nicolas Maduro.