Four million Venezuelans have now fled their country, UN aid agencies have reported, describing the speed of the migration in a joint statement as "staggering".
All but 700,000 of those have fled since the end of 2015.
Venezuela's economy has imploded and there are widespread shortages of food and medicine and there are also high levels of violent crime.
Around 3.2 million children - or one in three - need humanitarian assistance, the UN Children's Fund has reported.
And the crisis has deepened since the United States imposed sanctions, in its effort to oust leftist President Nicolas Maduro.
Washington has openly sided with the opposition leader Juan Guaido and dozens more nations around the world now recognise him as interim president.
They say Maduro rigged a 2018 election and is behaving like a dictator.
But Guaido has been unable to remove Maduro. He still has the backing of the top military brass and accuses his enemies of siding with Washington to bring about a coup.
US President Donald Trump's strong backing for Guaido hasn't tipped the balance and, meanwhile, the sanctions, which have failed to dislodge Maduro, have made the humanitarian crisis worse.