The Venezuelan crisis - pitting Maduro against opposition leader Juan Guaido, who is recognized by some 50 nations as the country's interim leader - has left Venezuelans facing dire shortages of food, medicine and other basics. She is scheduled to visit a border camp where Venezuelan migrants are staying in tents and hold a news conference in the Colombian region of La Guajira on Saturday.
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. But Maduro dismissed the aid as an infringement on Venezuela's sovereignty and prohibited it from entering.
Maduro had closed borders with Colombia, Brazil and Dutch Antilles islands as opposition leader Juan Guaido prepared to bring in USA -backed humanitarian aid. "We are a people of peace who firmly defend our independence", he wrote.
The report said the "alarming" number illustrates the urgent need to support neighboring states hosting refugees, such as Colombia (1.3 million), Peru (768,000), Chile (288,000), Ecuador (263,000), Brazil (168,000) and Argentina (130,000).
UNHCR said Friday that 4 million Venezuelans, or nearly 15% of the population, have left the country to escape its economic and political crisis.
Maduro announced on Friday that the border with Colombia, which has remained closed since late February, will be reopened in western Tachira State on Saturday. So far, the RMRP is only 21 percent funded. The chaos has been further aggravated by US sanctions on Venezuelan oil exports and has forced an estimated 5,000 people to leave the country each day, according to the United Nation's refugee agency.
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"The pace of the outflow from Venezuela has been staggering", the refugee agency UNHCR and the International Organisation for Migration (IOM) said in a joint statement.
Mexico and countries in Central America and the Caribbean are also hosting significant numbers of refugees and migrants from Venezuela.
Duque said he hoped Jolie's visit would alert the world to the seriousness of the migration crisis.
Speaking in Cartagena following a meeting with Colombia's President Ivan Duque, the actress said more than 20,000 Venezuelan children were at risk of statelessness. In the run-up to the attempt to smuggle in the cargo, Maduro closed the border, severing diplomatic relations with Colombia and expelling its diplomats from the country.
Maduro accuses his foes of plotting with Washington to bring about a coup.