Most Latin American and European countries also support Venezuelan opposition claims the Maduro government is now illegitimate, after it barred most opposition candidates from running in last year's election. Humanitarian assistance from the U.S.is in Colombia and is en route to the town over objections from Maduro, who blames the White House for leading a coup against him.
However, Guaido has rejected any negotiations, seeing it as a way for Maduro to buy time.
"We believe these to be those first couple pebbles before we start really seeing bigger rocks rolling down the hill", the official said this week, speaking on condition of anonymity.
Britain, Germany, France and Spain and more than a dozen other European Union member states recognised Mr Guaido in a coordinated action on Monday, following the expiration of an ultimatum they gave for Mr Maduro to hold a new presidential election.
The socialist president "could accept negotiations in exchange for the lifting of sanctions and relaxing of global pressure", according to Ernesto Pascual, political scientist at the Open University of Catalonia.
European nations have been broadly critical of Maduro but have sought to strike a counterpoint to the aggressive USA stance by urging dialogue.
But Maduro is still in control of the military and is using it as leverage to maintain power.
A Venezuelan migrant prays in the Divina Providencia migrant shelter in Cucuta, Colombia, on the border with Venezuela, on February 7, 2019.
Juan Caicedo, a spokesperson from Migration Colombia, Colombia's Ministry of Immigration and Immigration Control, said the Venezuelan military put the blockade into place Tuesday afternoon, adding that there are cameras monitoring activity on the bridge.
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In the Colombian border town of Cucuta, where the first USA aid arrived Thursday, the American ambassador called on the Venezuelan security forces to allow the aid in.
The US, which has not ruled out a military intervention in crisis-wracked Venezuela, was the first to recognise his rival as acting president, followed by a dozen Latin American countries.
Asked what would happen if the Venezuelan military blocks the aid from going in, Whitaker said any obstacles would be dealt with as they arise and reiterated that Trump has made clear nothing is off the table - though, he added, the priority is to arrange a broad worldwide mission. He was arrested last month after he entered Venezuela clandestinely from Colombia.
For analysts, the military holds the key to the crisis. "This would be the end of the revolution", Leon said, referring to the leftist ideology and government style of late president Hugo Chavez.
Venezuela's dire situation has fuelled a political crisis that has peaked over the last month with Guaido invoking a constitutional provision to declare himself the legitimate, interim president.
Pascual says it's "unthinkable" the armed forces would abandon Maduro "because of the high command's vested interests in oil and mining".
Their organization, the International Contact Group on Venezuela, issued a statement saying they would send a technical mission to the country to help provide humanitarian aid and support new elections as soon as possible.
"The military sector needs face-to-face negotiations" with specific officials, "an worldwide guarantor and probably a pardon being enshrined in the constitution", he said.
A day after the United States aid convoy arrived in the border city of Cucuta, Maduro ridiculed the Americans for offering small amounts of assistance while maintaining sanctions that block some $10 billion of offshore assets and revenue.
In Caracas, President Nicolas Maduro denounced the presence of trailers of humanitarian aid brought to the Colombian border, calling them part of a plan cooked up in Washington to destabilize his government.