President Juan Manuel Santos said Saturday he wanted to check that fellow Colombians were getting the "services they need" as he toured Cucuta, a city of 700,000 dependent on trade with neighboring Venezuela.
Santos was shown Colombians queuing for hours to get gasoline, while Mayor Donamaris Ramirez said most locals previously bought smuggled cut-rate fuel from oil-rich Venezuela, where supplies are subsidized.
Venezuela's President Nicolas Maduro closed border posts on August 19 after three Venezuelan soldiers were shot and wounded by two assailants on a motorcycle.
More than 1,000 Colombians have since been deported from Venezuela and others living in shanty towns say they fear that mass expulsions.
Maduro has already ordered the deployment of 3,000 troops to trace Colombian paramilitaries, whom he blamed for last week's shooting.
Venezuela itself is mired in a deepening economic crisis, made worse by a plunge in world prices for oil, its main source of hard currency.
Cucuta's mayor said he wanted to bring Maduro before the Interamerican Human Rights Commission over the expulsions of Colombians from Venezuela.
Previously, many people had routinely crossed the border to work, shop and visit relatives. An estimated 5 million Colombians live in Venezuela. Many have dual nationality.
Venezuelans grappling with chronic shortages say the border closures have interrupted supplies they normally find in Colombia.
The Red Cross has set up emergency housing on Colombia's side of the border. Permanent shelters are already overflowing.
Visiting the country's border region on Friday, Venezuelan Vice President Jorge Arreaza said "we're working to guarantee that everyone can live well from their work."
One departing Colombian, Martha Restrepo said she had decided to return to her home nation after living for 10 years in Venezuela without legal status.
"I'm going because I'm just fed up. I came here 10 years ago to work, and I'm leaving now because of what Maduro has been saying," she said.
The Organization of American States (OAS) plans to hold an emergency session on Monday to discussed the crisis.
ipj/bk (AP, AFP, dpa)