© Reuters. FILE PHOTO: Traders work at the Citadel Securities post on the floor of the NYSE

By April Joyner

NEW YORK (Reuters) - U.S. stocks rose on Wednesday, with the S&P 500 set to erase all its losses from Tuesday as signs of easing political turmoil in Italy emerged.

Italy's 5-Star Movement party made a renewed attempt to form a coalition government and called for eurosceptic economist Paolo Savona to withdraw his candidacy as economy minister.

The Italian government's successful auction of five- and 10-year bonds also assuaged concerns about the country's ability to finance itself after a sell-off in Italian bonds on Tuesday resulted in the biggest one-day surge for two-year yields in 26 years.

Fears about instability in Italy had sent investors scurrying to safety assets on Tuesday. U.S. stocks took a beating, with the S&P 500 posting its first 1 percent drop in May, while the U.S. Treasury market had its best day since at least July 2011.

"The market is reversing what appears to be a knee-jerk reaction from yesterday," said Keith Lerner, chief market strategist at SunTrust Advisory Services in Atlanta. "As people take a step back, it appears that the sell-off was overdone."

The Dow Jones Industrial Average ( ) rose 302.45 points, or 1.24 percent, to 24,663.9, the S&P 500 ( ) gained 34.81 points, or 1.29 percent, to 2,724.67 and the Nasdaq Composite ( ) added 69.01 points, or 0.93 percent, to 7,465.61.

The Russell 2000 index of small-cap stocks ( ) hit an all-time high during Wednesday's session, buoyed by data confirming the strength of the U.S. economy. Small-cap U.S. companies generally have less international exposure than their large-cap counterparts.

Payroll processor ADP's monthly report showed U.S. private sector payrolls increased by 178,000 jobs in May. The Commerce Department revised its estimate of first-quarter gross domestic product growth slightly downward but estimated that U.S. GDP growth in the second quarter would rise above 3 percent annually.

The S&P energy index ( ) jumped 3.2 percent and was on track for its biggest one-day gain in seven weeks.

Energy shares, which provided the biggest boost to the S&P 500, benefited from a 2.2-percent surge in oil prices. [O/R]

Cloud-based business software maker Salesforce.com (N: ) rose 2.1 percent and computer and printer maker HP Inc (N: ) jumped 4.2 percent after both companies raised their full-year profit forecasts.

Advancing issues outnumbered declining ones on the NYSE by a 4.48-to-1 ratio; on Nasdaq, a 2.78-to-1 ratio favored advancers.

The S&P 500 posted 28 new 52-week highs and two new lows; the Nasdaq Composite recorded 193 new highs and 28 new lows.