According to the BBC, Maduro said Venezuela would not be accepting the aid because it has "never been, nor are we, a country of beggars".
Diplomats said they expected the proposed measure to win at least nine votes in the council, forcing a veto to block its adoption.
On Monday, Pence flew to Colombia to meet with the internationally recognized interim President of Venezuela Juan Guaido and regional leaders to discuss how to further isolate the Maduro regime.
In addition to the USA resolution, Russian Federation is drafting a rival text, which reiterates the need to respect principles of the U.N. Charter such as sovereign equality, non-intervention in internal affairs and the peaceful settlement of disputes.
The US-drafted measure expresses support for "the peaceful restoration of democracy and rule of law in Venezuela" and requests that UN Secretary-General Antonio Guterres broker a deal on holding fresh elections. In order to pass, a resolution needs nine votes in favor and none of the five permanent members - the United Kingdom, the U.S., Russia, France and China - can oppose.
The United States is leading a push for recognition of Guaido, who heads the National Assembly, backed by about 50 countries.
By provoking a series of violent confrontations along the Colombian and Brazilian borders, the Trump-backed opposition has managed to manufacture a false narrative created to delegitimize the Maduro government and justify further foreign military intervention.
"If Beijing and Moscow kill it off, the United States will claim the moral high ground", said Gowan, a senior fellow at the UN University Centre for Policy Research.
Responding to threats against Guaido and others in the opposition, the draft "stresses the importance of ensuring the security of all members of the National Assembly, and members of the political opposition".
Venezuela's foreign minister on Wednesday called for direct talks between President Nicolas Maduro and Donald Trump to address the country's crisis - a proposal swiftly rejected by the White House, which recognises the opposition.
Maduro also "stands ready for dialogue" with the Venezuelan opposition, he said.
Guaido was to travel to Brasilia to meet President Jair Bolsonaro today.