About $1 million of the aid funding will go to the International Committee of the Red Cross for work on water and health systems, while the rest will go to the UN Refugee Agency. It comes after a $500,000 announcement earlier this year.
Peters also reiterated a call for Venezuelan President Nicolas Maduro to "respect the will of the people and hold fair and free elections", in reference to concerns about the integrity of the 2018 polls that gave Maduro a second term.
But Peters again avoided joining Western allies, including the United States, Britain and Australia, in recognising Venezuelan opposition leader Juan Guaido as interim president.
Amid protests, Guaido in January declared a rival presidency two weeks after Maduro was sworn in, although Maduro still holds on to power.
The National Party has said that by refusing to support Guaido, New Zealand is endorsing Maduro by default.
Peters has defended the Government's position, saying it was not New Zealand policy to make statements recognising governments and that it was up to Venezuelans to decide who their government was in a fair election.
Recent polling in Venezuela has shown that while public support for Guaido still remains high, it has declined since February.
Maduro took office in 2013 after the death of Hugo Chavez.