The Labor Department said its consumer price index increased 0.6% last month after surging 0.8% in April.
The labor market and inflation are two key factors for the Fed to consider tightening, and while inflation has risen, recent payrolls data was underwhelming.
ET, the Dow Jones Industrial Average (.DJI) was up 230.84 points, or 0.67%, at 34,677.98, the S&P 500 (.SPX) was up 27.27 points, or 0.65%, at 4,246.82.
read moreAdvancing issues outnumbered decliners by a 2.55-to-1 ratio on the NYSE and a 2.17-to-1 ratio on the Nasdaq.
The S&P index recorded 38 new 52-week highs and no new low, while the Nasdaq recorded 58 new highs and six new lows.
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