"I think oil's first, the trading range (in the S&P 500) is second, and what goes on in Asia is third," said Robert Pavlik, chief market strategist at Boston Private Wealth. "I think it's in that order. If oil can stabilize and not present an issue for the day then it becomes a range focus."
Oil briefly topped $30 a barrel before settling below at $29.53, up $1.18, or 4.16 percent, for its largest one-day gain since October.
The Nasdaq composite briefly turned negative during afternoon trade and never fully recovered earlier gains. The Russell 2000 ended mildly lower, while the iShares Nasdaq Biotechnology ETF (IBB) fell more than 2 percent. Recovery in both assets Wednesday afternoon helped lead a late-session recovery.
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Also weighing on the Nasdaq was a 5 percent decline in Netflix and half percent decline in Apple.
"Just a little profit-taking on a sell-off of oil under $30," said Peter Coleman, head trader at Convergex. "I'm still skeptical of the rally based on the fact the VIX never got to levels that justified the reversal in the market (Wednesday)."
Oil continued to hold near lows not seen since 2003. Weekly oil inventories showed a build in crude oil stocks and U.S. gasoline stocks. Distillate stocks showed a slight decline.
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"The data wasn't as bearish as the API data, so we got a little spike," said Daniel Flynn, analyst at The Price Futures Group. He also noted some short-covering and recovery from deeply oversold levels. The February contract settled 6.7 percent lower Wednesday amid volatility around the expiration of the contract at the close. WTI is down more than 20 percent year-to-date.
Data released late Wednesday by the American Petroleum Institute showed crude inventories rose by 4.6 million barrels, while the EIA reported commercial crude inventories rose by about 4 million barrels. Crude inventories climbed to the highest level since 1990.
"It looks like equities and oil are still closely tied, but at least they're moving in the right direction," Jack Ablin, chief investment officer at BMO Private Bank, said of morning gains in stocks.
"We could continue higher but I'd like to see the market drop a bit closer to fair value so we don't have any of the froth built in," Ablin said, noting that fair value for him is about 10 percent below morning levels in stocks.
U.S. stock index futures spiked Thursday morning, with Dow futures briefly up 100 points, on European Central Bank President Mario Draghi's remarks that downside risks have increased again and the central bank needs to review, possibly reconsider policy stance at the next meeting. Draghi also said the central bank has the power, willingness and determination to act, noting it has plenty of instruments, according to Dow Jones.
"If Draghi is actually going to talk about more liquidity, there's a potential ... that maybe the Federal Reserve is going to stop talking about raising interest rates," Pavlik said of the initial gains in futures.
The Federal Open Market Committee is scheduled to meet next Tuesday and Wednesday.
U.S. Federal Reserve Chair Janet Yellen will testify on monetary policy and the economy before the Senate Banking Committee on Feb. 11 and before the House Financial Services Committee on Feb. 10 for the U.S. central bank's semi-annual monetary policy report, Reuters said Thursday.
European stocks closed nearly 2 percent higher after Draghi's comments. Earlier, the European Central Bank kept rates unchanged.
Stocks closed well off session lows Wednesday, after the S&P 500 held the 1,800 level. However, the index still closed at its lowest level since April 2014. The Nasdaq composite also ended at its lowest level since 2014, while the Dow closed nearly 250 points lower at its lowest since August.
"There's a lot of cross-currents. My view is this is a growth scare, not a recession. The growth scares are magnified by moves in financial markets. If (a recession) is not the case, you 're starting to see some new values emerge," said Aaron Clark, portfolio manager at GW&K Investment Management.
He said strength in the banking sector supported a view that fundamentals remain intact. "For this to really have a negative transmission to the real economy, you need the banking system to be a risk," he said.
As of the close Thursday, the major U.S. indexes were on pace for a slight weekly decline but down about 8.5 percent or more for the year so far and more than 10 percent below their 52-week intraday highs, in correction territory.
Read MoreOil in charge, short-term relief coming for stocks?
In U.S. economic data, weekly jobless claims came in at 293,000, a six-month high. The January Philadelphia Fed index showed minus 3.5.
Treasury yields were mixed, with the 2-year yield a touch lower near 0.82 percent and the 10-year yield higher around 2.03 percent.
The U.S. dollar index held mildly lower against major world currencies, with the yen at 117.75 yen against the greenback. The euro traded just below $1.09 after briefly falling below $1.08 on Draghi's comments.
Asian stocks closed sharply lower overnight, with the Nikkei 225 off more than 2 percent and the Shanghai composite down more than 3 percent despite news China's central bank will inject more funds into money markets.
Read More Early movers: TRV, VZ, LUV, UAL, ALK, BBT, VIAB, CTXS, BCS & more
The Dow Jones industrial average closed up 115.94 points, or 0.74 percent, at 15,882.68, with Verizon leading advancers and Goldman Sachs the greatest decliner.
The Dow transports closed nearly 1 percent higher.
The S&P 500 closed up 9.66 points, or 0.52 percent, at 1,868.99, with energy leading seven sectors higher and financials and health care declining. Utilities closed flat.
The Nasdaq composite closed up 0.37 points, or 0.01 percent, at 4,472.06.
The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, held above 26.
About two stocks advanced for every decliner on the New York Stock Exchange, with an exchange volume of 1.2 billion and a composite volume of nearly 5.1 billion.
Gold futures for February delivery settled down $8.00 at $1,098.20 an ounce.
On tap this week:
Earnings: General Electric, Kansas City Southern, SunTrust, Legg Mason, Synchrony Financial, SAP
8:30 a.m.: Chicago Fed national activity index
9:45 a.m.: Manufacturing PMI
10 a.m.: Existing home sales
10 a.m.: Leading indicators
1 p.m.: Oil rig count
*Planner subject to change.
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