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 burning outposts and throwing rocks at soldiers and riot police in border areas.
Reporters at the scene have announced Mr Guaidó’s arrival at the Tienditas bridge on the Colombian side of the border. He was accompanied by the country’s president, Iván Duque.
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.
Those who do not allow aid to pass are “deserters” who “betray” the Venezuelan people, he added.
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.
“We want to work!” people chanted as they faced riot police at the Ureña border bridge.
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.
Earlier on Saturday, two people were killed by Venezuelan forces near the border with Brazil.