The U.S. dollar index was mildly higher with the euro near $1.139.
Treasury yields edged higher, with the 2-year yield near 0.73 percent and the 10-year yield around 1.77 percent.
"It seems just to be better risk sentiment to me," said Brandon Swensen, co-head of the fixed income desk at RBC Global Asset Management. "Looking across the board the risk-off fears are abating a bit."
The major stock indexes briefly gave up opening gains before extending gains as oil climbed.
"This is a tug of war going on between the bulls and the bears. You get profit-taking heading into earnings season. People get nervous," said Marc Chaikin, CEO of Chaikin Analytics.
The Nasdaq composite briefly turned lower as Starbucks temporarily declined more than 3.5 percent before closing 2.3 percent lower. Deutsche Bank downgraded the stock to "hold' from "buy" based on "lofty near-term investors' expectations" and "premium valuation."
"Earnings are kind of in a lull. The Fedspeak later in the day doesn't really matter because we know where they stand," Klein said. "It will be interesting to see today if there's another late-day sell-off."
The Dow Jones industrial average rallied more than 150 points on Friday and Monday only to reverse and close slightly higher or lower. The S&P 500 lost 5.61 points Monday to end in negative territory for the year so far, with consumer staples leading eight sectors lower.
"The S&P futures are range-bound from an intraday perspective, with each step forward seemingly met with one step back," BTIG Chief Technical Strategist Katie Stockton said in a morning note.
"The fickle price action reflects a loss of short-term momentum, which is made more concerning by widespread intermediate-term overbought conditions," she said. "A pullback has unfolded globally and short-term oversold conditions are still not widespread, affecting only 22 percent of the S&P 500 by our measures."
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In economic news, March import prices showed a 0.2 percent rise from the prior month for the first time in nine months, although the gain was well below the expected 1 percent rise. Export prices were unchanged.
U.S. small business confidence fell to a fresh two-year low in March at 92.6, amid persistent worries about sales and profits, Reuters said, citing the National Federation of Independent Business.
The major economic data due in the next few days include retail sales and inflation reports.
Early Tuesday, the International Monetary Fund trimmed its global growth forecast to 3.2 percent for 2016.
Speaking on CNBC's "Squawk Box" Tuesday morning, Dallas Fed President Robert Kaplan said the U.S. economy is likely to grow at just under 2 percent for the year. He also said the financial turmoil at the beginning of the year may have had more of psychological impact on consumers than previously thought.
Kaplan said Monday it is too soon for an interest rate hike in the United States, but he is open to a rate hike in June.
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Three other Fed officials spoke on Tuesday. Philadelphia Fed President Patrick Harker said in a Reuters report he supports raising rates again as the U.S. economy strengthens. He added it is still possible for the Fed to raise rates three times this year if the data allows.
Separately, San Francisco Fed President John Williams said in a Reuters report that with data on the U.S. economy coming in generally as expected, the Fed is on track to raise interest rates two or three times this year, He added he does not expect much market turmoil when rates do rise.
Richmond Fed President Jeffrey Lacker said recent signs that U.S. inflation is accelerating give the Fed a good reason to raise interest rates, Reuters reported.