* Greece submits new aid proposal to creditors
* Malta PM: Greece willing to suspend referendum if talks resume -report
* June U.S. consumer confidence rises more than expected
* Home prices rise slower than expected in April
* Indexes up: Dow 0.29 pct, S&P 0.46 pct, Nasdaq 0.71 pct (Adds comments, updates prices)
By Sinead Carew
June 30 (Reuters) - U.S. stocks turned positive around mid-afternoon in choppy trading on Tuesday as investors hoped for a last-minute deal to keep Greece in the euro.
Greece, hours from missing a 1.6 billion euro ($1.8 billion) payment due to the International Monetary Fund, 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.
After turning negative along with European equities, Wall Street reversed course after Malta's Prime Minister reportedly said Greece would be willing to suspend its planned referendum if talks resume.
"The market is just hinging on anything that comes out," said Mark Kepner, managing director, sales and trading at Themis Trading in Chatham, New Jersey. He cautioned that the report did not seem like "concrete news" and that stocks could fall again if more information comes out about Greece before the close.
"It all depends by the hour who says what," he said.
Volatility picked up on Tuesday also due to the expiration of quarterly options. The expiry of weekly options is a day early due to U.S. Independence Day holiday observance on Friday.
With roughly an hour of trading left for the day, the Dow Jones industrial average was on track to close negative for the first half of 2015.
On Monday, U.S. stocks had fallen sharply in heavy trading and the S&P 500 and the Dow had their worst day since Oct. 9 due to worries about Greece.
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 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.
A separate report showed the U.S. consumer confidence index rose more than expected to 101.4 in June. The consensus was for a reading of 97.3.
Investors are keeping a close watch on economic data for clues on the timing of an interest rate increase by the Federal Reserve, which has said it will raise rates when it sees a sustained rebound in the economy.
The Dow rose 50.32 points, or 0.29 percent, to 17,646.67, the S&P 500 gained 9.44 points, or 0.46 percent, to 2,067.08 and the Nasdaq Composite added 35.06 points, or 0.71 percent, to 4,993.53.
Eight of the 10 major S&P 500 sectors rose, with utilities and telecommunications services showing very slight declines.
For-profit education provider Apollo Education's shares fell 16.4 percent to $12.99 after the company reported lower-than-expected sales on Monday.
Signal Genetics shares surged 76 percent and was the biggest percentage gainer on the Nasdaq after it said it signed an agreement with a "leading" pharmaceutical company.
Advancing issues outnumbered declining ones on the NYSE by 2,061 to 1,013, for a 2.03-to-1 ratio on the upside; on the Nasdaq, 1,822 issues rose and 962 fell for a 1.89-to-1 ratio favoring advancers.
The benchmark S&P 500 index was posting 4 new 52-week highs and 23 new lows; the Nasdaq Composite was recording 25 new highs and 90 new lows. (Additional reporting by Siddharth Cavale in Bengaluru; Editing by Meredith Mazzilli)