"The situation is extremely critical as the heating season approaches," Novak said at a joint press conference with the EU's Energy Commissioner Guenther Oettinger.
"There is a high risk that gas delivered by Gazprom for Europe will be illegally taken by Ukraine for its own use," he warned.
Russia in mid-June cut its deliveries for Ukraine after a pro-Western government took power and disputes over prices led to what Novak said was the accumulation of a debt of USD 5.3 billion.
Russia is the EU's top supplier of gas. The 28-nation bloc depends on energy imports for more than 50 percent of its needs, and roughly 40 per cent of those imports are supplied by Russia.
Moscow has a history of using gas prices as a political weapon and has twice shut off supplies to Ukraine in the past decade, causing supply disruptions to Europe in 2006 and 2009.
Ukraine has recently acknowledged that it does not have sufficient reserves to make it through the winter and accused Russia of wanting to cut supplies to Europe.
For his part, Oettinger said that "to resolve the crisis one should not use gas as an instrument of sanctions and escalation."
He called for quickly creating a repayment schedule for gas delivered when prices were not under dispute.
Novak said that if Ukraine settles part of that debt, a "restructuring" of the other part could be considered.
Gazprom chief Alexei Miller, who was present during the talks, was quoted as saying by Russian news agencies that if some of the debt is repaid then it was willing to begin selling Ukraine gas on a pre-paid basis.