WTI crude oil fell through a key level of $45 a barrel twice on Tuesday, but recovered in late-morning trade and eventually closed at $45.89, causing some analysts to call another bottom on oil.

"$44 was my next target! If we close higher that could be it," said Phil Flynn, senior market analyst at The PRICE Futures Group. "If we close lower, we are targeting the Persian Gulf War high (about $38)."

Todd Gordon, founder of TradingAnalysis.com, said he expected WTI to find a support zone around $44/$43 with a target of $55 a barrel.

Oil's recovery from a morning low of $44.20 at around 6 a.m. New York time gave a boost to stock futures and many credited that with the lift in U.S. stocks Tuesday.

"We're on a long-term trend line right here right now, so I am expecting us to show some support at these levels," said John Caruso, senior market strategist at RJO Futures. His chart, tracking the lows since 1995, showed a bottom for oil around $45.52.

The $44.20 a barrel level is the lowest for WTI crude since March 2009. During the credit crisis, it traded as low as $35.40 a barrel in January 2009.

On Sunday, a report from Bank of America Merrill Lynch noted "two bullish developments for oil" to end last week. They are WTI futures approaching a 16-year trendline support level, which had stopped the decline of oil in 2009, and the slope of the oil futures curve, which is in contango, according to Merrill, and at "bearish extremes from which price lows have often coincided."

However, some energy pros and other traders were not so sure.

"There may some more to this bounce, but it is only temporary. There was damage done to the long-term chart off of the 2006 lows through present," said John Kilduff, energy analyst and co-founding partner of Again Capital. "A move to $33, the financial crisis low remains my downside objective."

Other analysts reminded that oil has broken swiftly all key support levels that have been pointed out by technical analysts over the last three months and so they don't expect a change until a fundamental move by the Saudi's or U.S. producers on the losing side of this trade. The commodity is down more than 57 percent since trading near $107 a barrel in June 2014.

"Oil has not bottomed," said Short Hills Capital's managing partner, Stephen Weiss. "Commodities only bottom when supply/demand metrics change. Nothing has changed on supply side in a meaningful way and demand side remains weak."

After Weiss' comments, the oil market did receive some encouraging news. The U.S. Energy Information Administration raised its 2015 world oil demand growth forecast by 120,000 barrels per day from its previous estimate.

The organization added in its monthly forecast that it expected 2016 world oil demand to hit 93.42 million barrels per day, up from 1.03 million from 2015.

PNC's energy analyst Paul Crovo said all the quantitative analysis is not sufficient for predicting an oil bottom. He once used Fibonacci analysis and other tools to predict a low in the high $40s, but now believes that only a geopolitical event or a move by OPEC will help restore oil prices.

He's keeping a close eye on a likely default in Venezuela's bonds, "an event that could signal a bottom." Moody's downgraded on Tuesday its debt rating on the country, which must pay billions of dollars in foreign debt this year and is considered the most vulnerable oil producer in OPEC.

To be sure, bullish traders were also talking about yet another fluke occurrence in the oil markets that should signal a bottom. The spread between WTI, the U.S. benchmark, and Brent, the European benchmark, was less than $2 a barrel Tuesday, its narrowest point since July 2013.

Whether this narrowing is a result of Europe's much slower economy or not, Brent should still trade at a higher premium based on logistics alone, traders said.

—CNBC's John Melloy and Reuters contributed to this report.