U.S. crude closed down slightly on Tuesday as investors fled to safe havens on worries about a near-bankrupt Greece and China's stock market losses and as technical selling threatened to push oil into a bear market.

Iran's determination to seal a nuclear deal with global powers to bring more of its crude to an oversupplied market and the restart of a key oil terminal in Libya also weighed on oil prices.

U.S. crude closed down 20 cents, at $52.33 a barrel, after falling almost $2 at the session low. Brent crude, on the other hand, rose 43 cents to $57 a barrel.

Investors fled to the relative safety of the dollar and U.S. bonds as Greek banks ran down to their last few days of cash after its people rejected international bailout while Chinese equities extended their hemorrhage, ignoring a slew of support measures from Beijing.

The dollar hit a five-week high, weakening demand for dollar-denominated commodities from users of other currencies.

"The U.S. dollar and Treasuries are what people are buying right now," said David Thomson, executive vice-president at Powerhouse, an energy-specialized commodities broker in Washington.

U.S. crude has lost almost 10 percent since Thursday's close for the sharpest two-day fall since 2011. It is teetering toward a bear market technically, having lost almost 20 percent from a high above $62 just a month ago. More downside momentum could push it to test the six-year low of $42.03 set in mid-March, technical analysts said.

"There has been a lot of money looking to pile into the short-side, and there have been an accumulation of different triggers to cue that over a short time. Some were looking at Iran; for some it is macro spill overs from Greece or China; for others it's a pure dollar play, and for others the rise in U.S. rig counts," said Paul Horsnell, head of commodities at Standard Chartered in London.

"None of those work in isolation, but put them all together in a short period and they'll do it. And after that, the technicals kick in to give a further push down."

The U.S. government on Tuesday modestly raised its 2015 and 2016 U.S. crude oil production forecasts while lowering its price outlook.

In its short term energy outlook, the U.S. Energy Information Administration raised its 2015 U.S. crude oil production growth forecast to 750,000 barrels per day (bpd) from 720,000 bpd.

The EIA forecast the average 2016 price for West Texas Intermediate crude, the U.S. benchmark, at $62.04 per barrel, a 5.4-percent drop from the previous monthly outlook.