About 5,000 Venezuelans flee their homeland daily, down from a peak of 13,000 in August, said Eduardo Stein, a joint special representative for the U.N. refugee agency UNHCR and the International Organization for Migration (IOM).
Stein described the two million figure as a planning estimate for migrants and refugees leaving for neighbouring countries in the next 14 months who will need aid.
"The region had to respond to an emergency that in some areas of concern was almost similar to a massive earthquake. We are indeed facing a humanitarian earthquake," he told a news briefing.
The U.N. appealed last week for $738 million in 2019 to help Venezuela's neighbours cope with the inflow of millions of refugees and migrants who have "no prospect for return in the short- to medium-term".
About 3.3 million Venezuelans have fled the political and economic crisis in their homeland, most since 2015, the UNHCR said.
About 365,000 of them have sought asylum, U.N. refugee boss Filippo Grandi said.
"The reasons these people left are ranging from pure hunger to violence and lack of security ... We at UNHCR believe many have valid reasons to seek international protection," he said.
Colombia has taken in one million Venezuelan nationals, with most others going to Brazil, Ecuador and Peru.
A bipartisan group of U.S. Senators proposed on Thursday giving temporary protected status to Venezuelan migrants to the United States.
Venezuelan President Nicolas Maduro blames its economic problems on U.S. financial sanctions and an "economic war" led by political adversaries.
The U.N. aid plan, presented to donors on Friday, aims to help Venezuelans to become productive contributors in host countries, said Antonio Vitorio, director-general of the IOM.
"This means focusing on access to the labour market, recognition of qualifications and also guaranteeing that the provision of social services in those countries - especially housing, health, and education - are up to the stress that derives from the newcomers," he said.