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, on Saturday.
Local media report people jumping the barricades to cross the border at the Venezuela-Colombia border, while opposition MPs have posted defiant messages on social media denouncing the use of force.
The BBC’s Orla Guerin, on the Colombia border, said Venezuelans were begging soldiers to be allowed to cross.
Pictures show protesters throwing rocks at soldiers and riot police in border areas.
Mr Guaidó urged the military to allow aid trucks to enter, calling on them to “put themselves on the side of the people“.
He confirmed that “various members” of the national guard had left their posts at the Simon Bolivar International Bridge to oversee the humanitarian aid delivery.
Three have abandoned post at this bridge, while another did so at the Paula Santander International Bridge in Ureña, in the south west of the country.
Earlier on Saturday, two people were killed by Venezuelan forces near the border with Brazil.
Mr Guaidó, who is the leader of the country’s opposition-dominated National Assembly, last month declared himself the country’s interim leader.
He has since won the backing of dozens of nations, including the US. He has called the rule of President Nicolas Maduro constitutionally illegitimate, claiming that Mr Maduro’s re-election in 2018 was marred by voting irregularities.
Venezuela is in the grip of a political and economic crisis. The country’s inflation rate has seen prices soar, leaving many Venezuelans struggling to afford basic items such as food, toiletries and medicine.
About 2.7 million people have fled the country since 2015.
Mr Guaidó says a lack of basic items has left thousands of others at risk of dying.