The data releases due Thursday include Fed Chair Janet Yellen's preferred indicator on the labor market, the Job Openings and Labor Turnover Survey for January.
"The labor market data now is somewhat secondary to the inflation data because we're near full employment," said Eric Stein, co-director of global fixed income at Eaton Vance Management.
Recent economic reports have showed signs of inflation picking up. The Labor Department on Wednesday said the consumer price index, ex-food and energy, rose 2.3 percent over the 12 months through February, Reuters reported.
However, in her news conference Wednesday afternoon, Yellen said, "There may be some transitory factors influencing" the recent rise in inflation.
Read MoreYellen: Negative interest rates not part of an active discussion
"I think markets continue to watch inflation. Markets are going to be continually assessing whether this pickup in core inflation is sustained," said Joe Seydl, capital markets economist at JPMorgan Private Bank. "All of the uncertainty right now is on the inflation side of the Fed's mandate."
"There's also the risk of another shock coming out of China," he said.
Other U.S. economic reports due Thursday include weekly jobless claims, the Philadelphia Fed survey for March, February leading indicators and fourth-quarter current account data.
Stocks rallied cautiously Wednesday after the Federal Reserve kept rates unchanged and lowered its projection to two hikes in 2016, down from four. Most analysts had expected a drop to three.
U.S. crude oil futures jumped 5.8 percent, or $2.12, to settle at $38.46 a barrel Wednesday, helped by the Fed news, a smaller-than-expected inventory build and the announcement of a meeting to discuss a proposal to freeze output.
Read MoreWall Street checks out of coal mines
Materials and energy led gains at the close. The Dow Jones industrial average and S&P 500 topped their 200-day moving averages to close at their highest of the year so far, with the Dow up 74 points to 17,325 and the S&P rising 11 points to 2,027. The Nasdaq composite climbed 35 points to 4,763 for its highest close since Jan. 6.
With Wednesday's gains, the Dow is down less than 1 percent year to date as is the S&P.
Krishna Memani, chief investment officer at Oppenheimer Funds, said the Fed made the right move Wednesday.
"I think the sentiment is still not bullish. I believe the Fed provides a bit of an impetus. The two combined keeps the market down the path of a modest rally," he said.
"I think this is an extension of the bull market. This is probably going to be one of the longest expansions we have ever experienced and the longest bull market we've ever experienced," Memani said.
Read MoreThe Fed under Yellen and the gold trade