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The head of the Organization of American States travelled to Colombia's border with Venezuela on Friday to denounce Venezuela's socialist "dictatorship" for causing a migrant crisis for the region.

OAS Secretary General Luis Almagro said countries in the Western Hemisphere should work together to provide relief to the droves of Venezuelans who every day are fleeing hyperinflation and food shortages in their homeland.

But, Almagro added, the ultimate solution to the crisis is to restore democracy in Venezuela.

"This is an immoral crisis," Almagro had said Thursday after meeting Colombian President Ivan Duque. "And it is marked by the (Venezuelan) government's indolence."

During Friday's visit to the border, Almagro met aid workers and government officials in the Colombian city of Cucuta, where schools and hospitals are struggling to cope with the influx of Venezuelan migrants.

The outspoken diplomat was stopped on the street and greeted by dozens of Venezuelan migrants who urged him to work for the "liberation" of Venezuela from tyranny.

"Cucuta is the city that best exemplifies the lies of Venezuela's dictatorship," Almagro said during his visit. "The humanitarian crisis created in Venezuela can be felt here like nowhere else."

According to the United Nations, more than 2.3 million Venezuelans have left their country in recent years.

Increasingly they are leaving with no money and are travelling on foot across South American countries like Colombia, Ecuador and Peru, in dangerous journeys that can take several weeks.

In northern Brazil, locals attacked Venezuelan migrants after a Venezuelan man robbed a merchant.

Almagro said the OAS has created a working group that will look at ways to help desperate migrants as well as their host countries.

OAS member states recently voted on a resolution that accuses Venezuelan President Nicolas Maduro of breaking his country's constitutional order when he got himself re-elected in May in a vote boycotted by opponents.

Colombia's foreign ministry, meanwhile, said Friday that it was investigating preliminary reports that 20 soldiers from Venezuela's National Guard illegally entered a remote Colombian river hamlet and captured three civilians.

Relations between both countries have been tense for years, but have not affected Colombia's policy towards Venezuelan migrants so far.

According to Colombia's government, almost 1 million Venezuelans are currently living in the country.