* Greece submits new aid proposal to creditors
* June U.S. consumer confidence rises more than expected
* Home prices rise slower than expected in April
* Indexes up: Dow 0.28 pct, S&P 0.36 pct, Nasdaq 0.61 pct (Adds comments, updates prices)
By Sweta Singh
June 30 (Reuters) - U.S. stocks gave up some of their gains in afternoon trading on Tuesday as investors remained on the edge, hoping for a last-minute deal to keep Greece in the euro.
Greece submitted a new aid proposal to its creditors, calling for debt restructuring in what seemed like a last-ditch effort by Athens to resolve its impasse with lenders.
The country is hours away from defaulting on a 1.6 billion euro ($1.8 billion) payment due to the International Monetary Fund, leaving global markets on tenterhooks.
Volatility picked up as Tuesday also marked the expiration of quarterly options. The U.S. Independence Day holiday, being observed on Friday, means the weekly options expiry is a day early this week.
"We will continue to see uncertainty and high levels of volatility going into the next couple of weeks until we have a more clear path of what may happen with Greece," said Omar Aguilar, chief investment officer of equities at Charles Schwab Investment Management in San Francisco.
The CBOE Volatility index, a measure of the premium traders are willing to pay for protection against a drop in the S&P 500, was up 0.6 percent at 18.97.
With just over two hours of trading left for the day, the Dow and the S&P 500 were set to close negative for the quarter.
On Monday, U.S. stocks fell sharply in heavy trading and the S&P 500 and the Dow had their worst day since October.
U.S. corporations have limited exposure to Greece, but investors are concerned about the fallout across Europe if the country exits the euro zone.
In Asia, Chinese stocks reversed course to end up 5.5 percent after the government and regulators stepped up efforts to halt a 20 percent slump in the past few weeks.
In U.S. data, single-family home prices rose in April from a year earlier but at a slower pace than forecast, a closely watched survey said on Tuesday.
U.S. consumer confidence index rose more than expected to 101.4. The consensus was 97.3.
Investors are keeping a close watch on data for clues on the timing of an interest rate increase by the Federal Reserve. The Fed has said it will raise rates when it sees a sustained rebound in the economy.
At 13:36 a.m. EDT the Dow Jones industrial average was up 48.55 points, or 0.28 percent, at 17,644.9, the S&P 500 was up 7.39 points, or 0.36 percent, at 2,065.03 and the Nasdaq Composite was up 30.17 points, or 0.61 percent, at 4,988.63.
Eight of the 10 major S&P 500 sectors were higher, with the materials index leading with a 0.67 percent gain.
McDonald's was the biggest drag on the Dow with a 0.6 percent decline.
For-profit education provider Apollo Education's shares fell 16.8 percent to $12.93 after the company reported lower-than-expected sales on Monday.
ConAgra Foods Inc rose 1.2 percent to $43.99 after the packaged foods maker said it would exit its struggling private label foods business.
Rival TreeHouse Foods Inc rose 9 percent and was among the top percentage gainers on the NYSE after analysts said ConAgra's private-label exit could provide a lucrative opportunity for TreeHouse.
Signal Genetics shares surged 60 percent to become the biggest percentage gainer on the Nasdaq after the company signed an agreement with a "leading" pharmaceutical company.
Willis Group Holdings shares pared some gains to rise 4.3 percent to $47.35 after the insurance broker said it would combine with financial services provider Towers Watson & Co. Towers Watson shares fell 2.7 percent.
Advancing issues outnumbered decliners on the NYSE by 1,907 to 1,126, for a 1.69-to-1 ratio on the upside. On the Nasdaq, 1,770 issues rose and 966 fell for a 1.83-to-1 ratio favoring advancers.
The S&P 500 index showed 4 new 52-week highs and 23 new lows, while the Nasdaq recorded 22 new highs and 88 new lows. (Additional reporting by Siddharth Cavale in Bengaluru; Editing by Saumyadeb Chakrabarty)