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DJI-NEW YORK, June 28 (Reuters) - U.S. stocks rose for a second day on Tuesday on optimism that a solution to Greece's debt crisis was near, although low volume indicated underlying nervousness in the market.

Buyers snapped up shares after the S&P 500's 7 percent swoon since April, mostly in commodities and technology shares, as investors raised their exposure heading into quarter-end and before earnings season in July.

The Dow Jones industrial average .DJI gained 145.13 points, or 1.21 percent, to 12,188.69. The Standard & Poor's 500 Index .SPX rose 16.57 points, or 1.29 percent, to 1,296.67. The Nasdaq Composite Index .IXIC added 41.03 points, or 1.53 percent, to 2,729.31.

NYMEX-NEW YORK, June 28 (Reuters) - U.S. crude futures rebounded on Tuesday to post the biggest one-day percentage gain in almost six weeks on optimism that Greece would move to resolve its debt crisis and a weaker dollar.

Investors shrugged off mixed economic data for the day, which showed consumer sentiment flagged in June on worries about jobs and income while the plunge in home prices showed signs of leveling off.

On the New York Mercantile Exchange, crude for August delivery CLQ1 settled at $92.89a barrel, gaining $2.28, or 2.52 percent, the biggest percentage rise since May 18, when prices ended up 3.3 percent. It traded $90.44 to $92.96.

CBOT-SOYBEANS-Soybean futures on the Chicago Board of Trade settled firm on Tuesday but well below the day's highs as declines in soymeal amid softening cash markets pared gains in soybeans, traders said.

Spillover strength from the corn and wheat markets, as well as crude oil,underpinned the market.

REGIONAL EQUITIES-BANGKOK, June 28 (Reuters) - Southeast Asian stock posted limited gains on Tuesday as relief over an outline French bank agreement on Greek debt helped revive sentiment and investors bought sectors seen as beneficiaries of domestic consumption, like banking stocks.

The mild market rebound came amid light volume, with average market turnover in the region falling to 0.8 times the 30-day average.

Late selling pulled the main Philippine index .PSI off four-week highs to end nearly flat and the Singapore index .FTSTI finished a tad higher, erasing early gains, with Malaysia .KLSE, Thailand .SETI and Indonesia .JKSE eking out small gains.

For all the volatility, Malaysia and Indonesia were among markets squeezing out gains in the first half, in part buoyed by demand for the consumer sector.
T
he MSCI index of Malaysia .MIMY00000PMY had risen 3.1 percent so far this year and the MSCI index of Indonesia .MIID00000PID had gained 3.6 percent, against a 2.8 percent loss for Asian stocks outside Japan.

Indonesia gained a mild $7.2 million in inflows on Tuesday, outpacing $12 million worth of outflows of the Philippines, according to Thomson Reuters data.