US STOCKS-Wall St off session lows as Greece aid deal optimism grows

* IMF says will help Greece if asked, ECB holds call

* Tsipras to present aid proposal at euro zone meet Tuesday

* Aetna (NYSE: AET - news) falls after Humana (NYSE: HUM - news) deal, other insurers lower

* Energy index leads losses as oil prices fall

* Indexes down: Dow 0.2 pct, S&P 0.29 pct, Nasdaq 0.3 pct (Updates to early afternoon)

By Tanya Agrawal

July 6 (Reuters) - U.S. stocks were lower in early afternoon trading, but were well off their lows earlier on Monday as investors remained optimistic that a deal could be reached to prevent Greece's exit from the euro zone.

Greeks rejected the conditions of a rescue package from creditors on Sunday and the country's finance minister resigned on Monday, removing a major obstacle to any deal. Prime Minister Alexis Tsipras agreed to present an aid proposal at an emergency euro zone meeting on Tuesday.

Stock markets globally fell, but analysts said the declines were less than expected due to expectations that the European Central Bank would act to limit any damage.

U.S. stocks opened more than half a percent lower, but pared some of those losses, even turning positive briefly, after the International Monetary Fund said it is ready to assist Greece if asked.

"The referendum doesn't really change anything with the negotiations," said Mark Luschini, chief investment strategist at Janney Montgomery Scott in Philadelphia.

"I think after the initial knee jerk reaction, the majority opinion is that there is still a possibility of some sort of a deal that keeps Greece in the euro zone."

Greece's immediate fate is in the hands of the ECB, which began a conference call late afternoon to decide how long to go on keeping Greek banks afloat. Several people familiar with ECB policy said it would probably reject a Greek request to raise a cap on emergency liquidity assistance.

U.S. economic growth prospects got a boost after data from the Institute for Supply Management showed the pace of growth in the U.S. services ticked higher in June after dropping in May. The Federal Reserve has said it will raise rates only when it sees a sustained economic recovery.

At 13:03 p.m. ET the Dow Jones industrial average was down 35.47 points, or 0.2 percent, at 17,694.64. The S&P 500 was lower by 6.01 points, or 0.29 percent, at 2,070.77. The Nasdaq Composite was down 14.89 points, or 0.3 percent, at 4,994.32.

All the 10 major S&P 500 sectors were lower. The energy index led the declines with a 0.73 percent fall as oil prices slumped more than 6 percent after the Greek referendum and on a strengthening dollar.

Chevron's shares dropped as much as 1.5 percent to $94.48, its lowest since November 2011.

Health insurer Aetna fell 7.3 percent to $116.40 after it said it would buy smaller rival Humana for about $37 billion. Humana rose 2 percent to $191.38.

The deal is sure to face rigorous antitrust scrutiny, which could also make other large-scale mergers in the sector more difficult. Anthem (NYSE: ANTM - news) , Cigna (NYSE: CI - news) , Centene (NYSE: CNC - news) and Health Net (NYSE: HNT - news) , which are all in takeover talks, were lower.

Weight Watchers soared 17.6 percent to $4.81 after the New York Post reported an activist hedge fund was in talks with potential partners to buy the company. The hedge fund and a partner "would like to offer perhaps double" Thursday's closing price, the report said.

Declining issues outnumbered advancing ones on the NYSE by 1,932 to 1,057. On the Nasdaq, 1,664 issues fell and 1,041 advanced.

The S&P 500 index showed four new 52-week highs and 27 new lows, while the Nasdaq recorded 32 new highs and 113 new lows. (Editing by Savio D'Souza)