Soldiers from the Venezuelan National Guard have left their posts ahead of an opposition-led effort to bring aid into the country, Colombia’s migration agency said.
In a separate development, Venezuelan troops have fired tear gas at people looking to cross into Colombia to work.
Tensions have been rising over a row about the delivery of humanitarian aid.
President Nicolás Maduro said the border with Colombia is partly closed to stop aid being delivered.
But self-declared interim president Juan Guaidó has vowed that hundreds of thousands of volunteers will help bring in the aid deliveries, which include food and medicine.
The first delivery of aid has already entered Venezuela through Brazil, Mr Guaidó tweeted.
The delivery of aid to the stricken country has proven to be a key area of contention between the two men who see themselves as Venezuela’s leader.
Pictures at various crossing points show security forces firing tear gas at volunteers and protesters burning outposts and throwing rocks at soldiers and riot police.
On the Venezuela-Colombia border, at least thirteen members of the security forces defected on Saturday, Colombia’s migration authority said.
A video posted on social media appears to show four soldiers publicly denouncing Mr Maduro and announcing their support for Guaidó.
Local media report people jumping the barricades to cross the border, while opposition MPs have posted defiant messages on social media denouncing the use of force.
Venezuelans were begging soldiers to be allowed to cross, at the Simon Bolívar International Bridge.
Mr Guaidó visited the Tienditas bridge on the Colombian side of the border, where he was accompanied by the country’s president, Iván Duque.
“Welcome to the right side of history”, he told soldiers who had abandoned their posts, adding that soldiers who joined them would be guaranteed “amnesty.”
“We want to work!” people chanted as they faced riot police at the Ureña border bridge in south-west Venezuela.
Activists there were joined by 300 members of the “Women in White” opposition group who marched in defiance of Mr Maduro’s attempts to close the border.
Meanwhile, a top ally of President Maduro has suggested the government would allow Venezuelans to accept aid “at their own risk”, but that no foreign soldiers would “set foot” inside Venezuela.
The president himself tweeted that “there will not be a war”, posting pictures of cheering crowds in Caracas.
“Take your hands off Venezuela, Donald Trump”, he told crowds, accusing the US president of using aid as a means to invading the country.
He accused Mr Guaidó of being a “puppet”, and “American pawn”, a “clown” and an “imperialist beggar.”