Geopolitical concerns trumped economic fundamentals in Tuesday trading in New York as major crude oil indices rallied 2 percent from the previous close.

Crude oil prices were volatile for Monday after Saudi Arabia hinted it was ready to cooperate with other producers wary of a depressed oil economy. Wealthy producers like Saudi Arabia have kept output steady even as supplies build, putting downward pressure on crude oil prices. That's strained the economies of weaker producers like Venezuela and comes at a time when more oil could flood the market from a post-sanctions Iran.

Geopolitical tensions, meanwhile, remain high in the wake of recent terror attacks in France, Lebanon, Mali and elsewhere. Late Tuesday, the U.S. State Department warned of a "possible" risk to American citizens traveling overseas.

Russian President Vladimir Putin, meanwhile, reacted angrily to the downing of a Russian military jet near the border between Turkey and Syria, calling it a "stab in the back" by the Turkish forces said to have shot it down.

Oil prices rallied in part in response to security issues. Brent crude oil gained 2.3 percent to $45.88 per barrel in early Tuesday trading. West Texas Intermediate, the U.S. benchmark price for crude oil, rallied 2 percent to $42.55 per barrel.

For the economy, the U.S. Commerce Department said real gross domestic product increased at an annual rate of 2.1 percent for third quarter 2015. That beats the previous estimate of 1.5 percent, but is still below the 3.9 percent growth rate recorded during the second quarter.

Soft demand, a situation reflected by slow growth in the global economy, is leading to a buildup of crude oil supplies on the market.

Industry research group Genscape said in a research note there's a bottleneck of oil vessels in the U.S. waters of the Gulf of Mexico.

"Crude seemingly continues to be oversupplied in the region," it said.