WTI futures for March delivery, which expires Monday, settled down $1.13 at $29.64 a barrel but ended the week slightly higher. Oil pared losses after the U.S. oil rig count showed a decline of 26 in the last week, Baker Hughes said.
Futures for April delivery settled down $1.18 at $31.75 a barrel.
"I think when you look at today's market action it's more a story of oil than the Fed and CPI, but the CPI was one element to today's market action because in the back of people's mind the possibility there could be a rate hike down the road (rises) if the economic data continues to trend upward," said Kevin Nicholson, chief risk officer at RiverFront Investment Group. "We need to see oil stabilize above $30."
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The major U.S. averages ended the week up 2.5 percent or more, with the Dow Jones industrial average and S&P 500 posting their best week since the one ending Nov. 20. The Nasdaq composite outperformed, up nearly 4 percent for the week, its best since the one ending July 17.
"You've had a little bit of an emotional relief that will tend to shore up the market in the short-term," said Bruce McCain, chief investment strategist at Key Private Bank. "You just need a continued flow of ... news that beats expectations, less bad than expected."
In economic news, the consumer price index showed a 0.3 percent rise ex-food and energy in January. The headline figure was unchanged from the previous month. Year-over-year, the core CPI advanced 2.2 percent, the largest rise since June 2012, Reuters said.
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"The CPI number doesn't surprise me but it does surprise me the market isn't taking a closer look at it," said David Kelly, chief global strategist at JP Morgan Funds.
"I think it's an important report because it should remind people that underlying inflation pressures are moving up," he said.
U.S. stock index futures indicated a slightly higher open, before erasing gains and holding lower after the data release.
Treasury yields held higher, with the 2-year yield at 0.74 percent and the 10-year yield at 1.75 percent in afternoon trade.
The S&P 500 held mostly lower in afternoon trade after briefly attempting gains. Energy was among the greatest decliners in the index but pared losses in the close to end 0.35 percent lower.
"I think it's technical. The market ran into resistance at 1,950 (on the S&P 500)," said Marc Chaikin, CEO of Chaikin Analytics.
"In a market that's highly volatile and seemingly irrational, the only thing you have to go on are your technicals.," he said, attributing much of the recent gains to short covering.
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Boeing was the greatest contributor to declines on the Dow Jones industrial average, which closed about 21 points lower after briefly dipping 100 points in morning trade.
JJ Kinahan, chief strategist at TD Ameritrade, said he was surprised by the muted afternoon action since Friday was an options expiration day, which usually sees more volatility.
The Nasdaq composite turned positive in mid-morning trade and closed higher, helped by gains in Applied Materials, Facebook and shares of Alphabet, Google's parent company.
"So far the market's bouncing almost perfectly to work off the oversold conditions we saw last week. There's still a whole lot of overhead resistance," said Adam Sarhan, CEO of Sarhan Capital.
Cleveland Fed President Loretta Mester said Friday that policy will likely need to remain accommodative "for some time" given slow growth abroad, the strong dollar, more restrictive financial conditions and the hard-hit energy sector, Reuters reported. Mester also said Inflation will remain "lower for longer" than previously thought, although the U.S. economy will "work through" market volatility and soft economic data.
Read MoreGlobal interest rates: How does the Fed stack up?
The U.S. dollar index was little changed in late trade, with the euro near $1.113 and the yen at 112.64 yen against the greenback. Sterling strengthened against the dollar.
British Prime Minister David Cameron was negotiating with EU leaders in Brussels about the U.K.'s membership in the union. The talks were continuing after the European market close.
After the U.S. market close, Cameron said he "negotiated a deal to give the U.K. special status in the EU" and he believed it is enough to recommend Britain stay in the union.
Art Hogan, chief market strategist at Wunderlich Securities, earlier said the lack of resolution is "one of the overarching things that doesn't get enough attention" although it's "manifesting itself more in the European market."
European stocks closed lower amid the negotiations and declines in oil. However, the German DAX gained more than 4.5 percent for the week, its best since October.
Asian stocks were mostly lower Friday, but the Nikkei 225 ended the week with gains of nearly 6.8 percent for its best week in more than a year—since October 2014. The Shanghai composite was up about 3.5 percent for the week, its best since mid-December.