Russia resumed gas supplied to Ukraine less than two months ago after the two countries signed a deal ensuring supplies through March next year.
Russian news agencies on Tuesday quoted Novak as saying that Ukraine has pre-paid for gas only once since and that Moscow would have to cut off supplies "today or tomorrow".
Past gas disputes between Russia and Ukraine have led to cutoffs. One standoff in 2009 caused serious disruptions in shipments EU countries in the dead of winter. Temperatures in Ukraine can drop to as cold as -4 degrees Fahrenheit (-20 degrees Celsius) in winter, and most homes in Ukraine rely on piped gas for central heating.