The clashes began after Venezuelan troops blocked United States aid convoys - which Maduro sees as an attempt to undermine his government - from entering the country.
Venezuela's President Nicolas Maduro attends the celebration of the International Peoples' Assembly in Caracas, February 26, 2019.
Reuters quoted diplomats as saying the USA version is likely to receive the required nine votes in the council but is expected to fail due to a Russian veto.
Russian Federation had circulated a rival draft resolution "expressing concern over the threats to use force" against Venezuela and "to intervene" in its domestic matters.
The United States and dozens of other nations have recognised opposition leader Juan Guaido as Venezuela's legitimate president, but Maduro still controls the military, state institutions and oil company Petroleos de Venezuela SA, which provides 90 percent of the country's export revenue.
The United States has denied Russian accusations of planning military intervention in Venezuela, despite President Trump saying "all options are on the table". A revised US draft, seen by Reuters, was circulated on Wednesday.
"The "humanitarian aid" this weekend was a public relations stunt, since the aid was just a tiny fraction of the food and medicine that they are depriving Venezuelans of with the sanctions", Weisbrot said.
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As time marches on and this becomes clearer to our MPs, the risk is that they do, in the end, cave in to Mrs May's bad deal.
The final US draft doesn't mention the use or threatened use of force but it does make several references to peace.
Earlier at the Geneva forum, an aide to Colombian President Ivan Duque called for action to end Venezuela's humanitarian crisis and bring about a political transition leading to free elections. "For democracy to return and for Venezuela to rebuild-Maduro must go #VenezuelaLibre" Pence tweeted Wednesday afternoon.
The U.S. draft asks U.N. Secretary-General Antonio Guterres to help ensure there is a free, fair and credible presidential election with worldwide observers.
The Russians, however, are likely to object to another statement in the new USA text.
The US-drafted measure "stresses the importance of ensuring the security" of all lawmakers and opposition members, but a reference in a previous draft expressing "full support" for the National Assembly was dropped.
The delegations from the U.S., Argentina, Australia, Chile, Colombia, Peru, Canada, Israel and Argentina left the hall when Arreaza started began speaking. Belandria has been recognized as Venezuela's top diplomat by Bolsonaro's government.
A competing Russian text urges a peaceful settlement of the crisis and recalls that aid deliveries to Venezuela require the consent of Maduro's government.