Venezuelan border guards dressed in green uniforms helped to control the crowds.
Most of the aid was donated by the United Sates but rejected by Maduro, who said it was part of a plot to strengthen the opposition. From some 695,000 at the end of 2015, the number of refugees and migrants from Venezuela had skyrocketed to over 4 million by mid-2019, according to data from national immigration authorities and other sources.
The decision to reopen a section of the border with Colombia follows Maduro's decisions last month to reopen the border with Brazil and the Caribbean island of Aruba, which were also closed amid concerns the opposition would attempt to breach them on the pretext of bringing in "humanitarian convoys".
Many citizens have resorted to illegal crossings over backroads, at times paying tolls to criminals who controlled passage, in order to get groceries or basic medical treatment.
Following the visit, the Colombian president, whose country has received 1.3 million refugees from Venezuela, said he hoped Jolie's visit would raise attention to the seriousness of the migration crisis.
The latest increase has brought the total number of Venezuelan migrants and refugees overseas to 4 million, up from 695,000 in late 2015, when the opposition's election victory set the stage for intensifying conflict with President Nicolas Maduro.
The report-published by the United Nations refugee agency and the International Organization for Migration-said the rate of exodus had rocketed since the end of 2015, when the figure stood at 695,000.
"These alarming figures highlight the urgent need to support host communities in the receiving countries", said Eduardo Stein, joint UNHCR-IOM Special Representative for Venezuelan refugees and migrants.
The once-wealthy oil nation is now facing severe shortages of basic goods and hyperinflation that is expected to surpass 10 million percent this year, according to a recent International Monetary Fund estimate.
He, Jolie and UNHCR officials had a productive meeting on Saturday morning, Duque said, including a discussion about how to nationalize the stateless children.
Relations between Venezuela and Colombia, who share a land border stretching 2,220 kilometres, have been broken since February 23 when Duque announced his support for Guaido.