Signs of progress in reducing tensions in the Middle East, after a Russia-brokered deal on Syria's chemical weapons also helped to support stocks.
Summers' surprise decision on Sunday came just ahead of the Fed's policy meeting on Tuesday and Wednesday, when the U.S. central bank is expected to begin to scale back its asset purchases from the current pace of $85 billion a month.
With the withdrawal of Summers, investors wagered that U.S. monetary policy would stay easier for longer if the other leading candidate for Fed chair, Janet Yellen, the Fed's current vice chair, should get the job. Ben Bernanke's term as Fed chairman expires in January.
The Dow Jones industrial average <.dji> was up 117.88 points, or 0.77 percent, at 15,493.94. The Standard & Poor's 500 Index <.spx> was up 9.62 points, or 0.57 percent, at 1,697.61. The Nasdaq Composite Index <.ixic> was down 4.34 points, or 0.12 percent, at 3,717.85.
The Nasdaq stock index rose for much of the session, but turned negative in afternoon trading, pressured by a 3.2 percent decline in Apple Inc
"We are still riding positively on the Summers announcement, however with the debt ceiling deadline less than a couple of weeks away, there will be heightened sensitivity to it," said Andre Bakhos, managing director at Janlyn Capital LLC in Bernardsville, New Jersey.
"We are still up and the market is still riding a wave higher and until there is something tangible to create a sense of fear, the trend remains solid."