* Apple up after bond pricing, sets market cap record
* U.S. Dec. job openings hit highest level since Jan. 2001
* Indexes up: Dow 0.79 pct, S&P 1.07 pct, Nasdaq 1.3 pct (Updates to the close of trading)
By Sinead Carew
NEW YORK, Feb 10 (Reuters) - U.S. stocks rose on Tuesday on hopes that Greek debt negotiations could result in a deal that stabilizes Europe, while Apple helped lift the S&P 500 and Nasdaq as it became the first U.S. company worth more than $700 billion.
Apple Inc shares closed up 1.9 percent to $122.02 after it priced Swiss franc bonds.
S&P 500 utilities were the day's strongest sector, after declining the day before, and the energy sector pared losses despite a slump in crude prices.
Investors focused on news from Greece and Ukraine, said Adam Sarhan, chief executive of Sarhan Capital in New York.
"Today you're bouncing off a 50-day moving average, which is a pure technical play. The fundamentals are improving a little bit because the situation in Ukraine did not explode. That was a concern over the weekend. Also, Greece hasn't fallen off the radar," Sarhan said.
The European Commission said there was no formal proposal for resolving Greece's debt problems, although talks were intensive ahead of a series of meetings of euro zone finance ministers and EU leaders in Brussels.
But the Commission is expected to introduce a compromise proposal, according to a report by MNSI, citing unnamed sources.
"You have a headline-driven market that moves every time there's a headline on Greece," said Joe Saluzzi, co-manager of trading at Themis Trading in Chatham, New Jersey. "It doesn't shock me, yet it doesn't make any sense."
The Dow Jones industrial average rose 139.55 points, or 0.79 percent, to 17,868.76, the S&P 500 gained 21.85 points, or 1.07 percent, to 2,068.59 and the Nasdaq Composite added 61.63 points, or 1.3 percent, to 4,787.65.
The U.S. Labor Department said job openings surged to 5.03 million in December, the highest level since January 2001. In contrast, Halliburton said it could cut more than 6,000 jobs due to low oil prices.
The first drop in crude prices in four sessions pushed the energy index down as much as 1.9 percent before it closed down 0.2 percent. U.S. crude prices fell about 5 percent after the International Energy Agency warned of more selloffs in the near term as stockpiles rise.
About 6.5 billion shares changed hands on U.S. exchanges, below the 7.5 billion average for the last five sessions, according to BATS Global Markets.
Advancing issues outnumbered decliners on the NYSE by 1,739 to 1,324, for a 1.31-to-1 ratio; on the Nasdaq, 1,678 issues rose and 1,070 fell, a 1.57-to-1 ratio.
The benchmark S&P 500 index posted 29 new 52-week highs and 3 lows; the Nasdaq Composite recorded 57 new highs and 38 lows. (Additional reporting by Chuck Mikolajczak; Editing by Jeffrey Benkoe, Nick Zieminski and Chizu Nomiyama)