U.S. oil closes up 69 cents, or 1.94%, at $36.31 per barrel

What the crude crash means for consumers and Big Oil
What the crude crash means for consumers and Big Oil
Here's what's causing oil prices to fall
Here's what's causing oil prices to fall
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Weak oil good for consumers
Outlook for oil: The view from the Middle East
Outlook for oil: The view from the Middle East

U.S. crude rose nearly 2 percent Monday, recovering slightly after moving within a hair of 11-year lows, as record short interest led to technical covering on fears that the market declined too quickly.

Early in the day, both Brent and U.S. crude futures fell by as much as 4 percent to their lowest levels since the start of the 2008 financial crisis, before paring losses on some short covering. 

At the close, U.S. crude was up 69 cents, or 1.94 percent, to $36.31 a barrel. 

John Kilduff, partner at Again Capital, said the market might have found a bottom. "We had gone so far so fast that it was just time," he said.

However, Kilduff said he expects crude to near lows again in late February when the Spring refinery maintenance season gets under way.

At Monday's close, Brent futures were down 0.45 percent, at $37.76 a barrel. 

Earlier in the session, Brent traded just 13 cents above the $36.20 low set in December 2008. Below that level, Brent would be at its lowest since July 2004 — a year when oil was rebounding from single-digits lows hit during the 1998 financial crisis and when talk of a commodities super-cycle was just beginning.

"If you look at a 10-year chart, I think what you'll see is going back to 2008, that December low of $32.40, that's going to be the next big level to watch here," Mike Harris, president of Campbell & Co., told CNBC on Monday. "If we get through there, then you know the $30 psychological level will be the next big level for the market to breach." 

OPEC has been pumping near record levels since last year in an attempt to drive higher-cost producers such as U.S. shale firms out of the market. U.S. output has fallen though not by much, while production from Russia — another big non-OPEC player — has risen.

OPEC supply is likely to increase by 1 million barrels per day next year, Morgan Stanley said in a research note.

"Almost the entirety of added supplies in 2016 will come from Iran, Iraq and Saudi," it said.

Iran has promised to ramp up supply once nuclear-related sanctions are lifted on its crude exports. Tehran is expected to raise crude and condensates exports by as much as 700,000 bpd by the end of 2016.  

"The news on the supply side continues to be that there's a glut out there. IEA on Friday saying that the oil glut will last until at least late 2016," Harris said on "Fast Money: Halftime Report." "Then you have the Iran deputy oil minister throwing oil on the fire, so to speak, with his comment about absolutely no chance of delaying the output increase." 

Harris said as long as the price trend continues to the downside, he'll continue to stay short oil. 

— CNBC's Ritika Shah contributed to this article.