Analysts also noted markets remain on edge ahead of the potentially historic Federal Reserve meeting next week, when the central bank could raise rates for the first time in nearly a decade.
"In many ways the market is trying to move beyond oil to next week's event, which is the Fed," said Dan Farley, regional investment strategist for The Private Client Reserve at U.S. Bank.
"The biggest short-term risk to the market is they don't raise," he said.
As of the close Thursday, CME's FedWatch tool showed markets are pricing in a more than 80 percent chance of a December hike.
The Fed "has been such an anticipated event people are on the edge of their seats for no reason," said JJ Kinahan, chief strategist at TD Ameritrade. He noted the VIX is up about 30 percent for the week so far, indicating "there's still a lot of nervousness in the market."
The CBOE Volatility Index (VIX), widely considered the best gauge of fear in the market, held little changed near 19.
Stocks kicked off Thursday's session mixed, with the S&P 500 and the Nasdaq composite trading slightly positive, and the Dow Jones industrial average lower. The three major indexes later tried for gains.
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On Wednesday, U.S. stocks closed lower in choppy trade as oil prices weighed and as investors tried to position themselves ahead of a possible Fed rate hike. The Dow gave up triple-digit gains and dropped over 150 points at its lows.
"I think we're seeing a market that is discounting a Fed rate hike ... and lower oil prices," said Peter Cardillo, chief market economist at First Standard Financial. "From a technical perspective, the S&P 500 managed to hold the 2,040 level."
Investors also digested two economic data sets Thursday morning, with initial jobless claims rising to 282,000. Economists polled by Reuters expected the number to come in at 269,000.
"The level of firings remains muted as in a tight labor market with near 40 year lows in participation employers are holding tight to the employees they have (outside of energy and manufacturing)," Peter Boockvar, chief market analyst at The Lindsey Group, said in a note.
Meanwhile, import prices fell 0.4 percent in November, as oil prices weighed, the Labor Department said.
Treasury yields held mostly higher, with the 2-year yield at 0.96 percent and the 10-year yield at 2.23 percent in the close.
The U.S. dollar recovered from a dip to trade about half a percent higher against major world currencies, with the euro holding above $1.09 and the yen at 121.62 yen against the greenback in the close.