Long lines of Venezuelans stood at two global bridges near the city of Cúcuta waiting to have their documents checked by Colombian officials.
The Venezuelan government in May reopened its land border with Brazil and the sea route with Aruba, but not with other islands such as Bonaire and Curacao. "We are a people of peace who firmly defend our independence", he wrote.
Maduro's announcement caused worry in Colombia, Rampietti said, with "a number of mayors and governors of Colombian regions on the border called for a national security meeting, fearing an increase in the pace of the exodus of Venezuelans".
Maduro said the assistance was part of a plot to strengthen the opposition and blocked it from entering.
Duque said that during the meeting with Jolie and UNHCR officials, both sides discussed steps that could be taken to facilitate the integration of Venezuelan migrants and refugees in Colombia, including legislation to grant Colombian nationality to thousands of children of Venezuelan migrants who have been born in Colombia and are now stateless. Parents of children born overseas have been having trouble registering the birth of their children.More news: Facebook's GlobalCoin to go live as early as in June
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The previous United Nations count was 3.7 million and the "alarming" new figure highlights the urgent need to support host countries, mainly in Latin America - led by Colombia with 1.3 million and followed by Peru, Chile, Ecuador, Brazil and Argentina, it said.
"The president and I spoke of the risk of statelessness for more than 20,000 Venezuelan children, his commitment to always helping children", Academy Award-winner Jolie, 44, said at a press conference.
Duque said he hoped the visit would alert the world to the seriousness of the migration crisis.
To complement these efforts, a humanitarian Regional Refugee and Migrant Response Plan (RMRP) was launched last December, targeting 2.2 million Venezuelans and 580,000 people in host communities in 16 countries.
Mr. Maduro says Venezuela is victim of an "economic war" led by the opposition with the help of Washington, which has levied several rounds of sanctions against his government.