* AIG shares slide after posting decline in earnings
* Office Depot to close 400 U.S. stores; shares up 16 pct
* Einhorn bets Athenahealth will fall, traders sell
* Indexes down: Dow 0.8 pct; S&P 0.9 pct; Nasdaq 1.4 pct (Updates to close)
By Rodrigo Campos
NEW YORK, May 6 (Reuters) - U.S. stocks fell broadly on Tuesday, closing at session lows, with AIG pulling financial shares lower after disappointing earnings and as a slide in Twitter took down other names in the technology and internet space.
Traders also kept an eye on developments in Ukraine, where supporters of Russia and of a united Ukraine are accusing each other of tearing the country apart. The former Soviet republic is sliding toward war.
"The short-term issue is Ukraine. We don't know when we'll wake up one morning and (Russian President Vladimir) Putin is going to be in eastern Ukraine," said Jack De Gan, chief investment officer at Harbor Advisory Corp in Portsmouth, New Hampshire.
Twitter shares tumbled 17.8 percent to $31.85 after the expiration of a six-month "lock-up" period that had restricted the sale of about 82 percent of its outstanding stock.
The rout was in the busiest trading day for the stock so far as more than 134 million shares changed hands, above the near 118 million shares traded on its debut. The 10-day volume average was just under 16 million.
The S&P 500 is just 1.2 percent below its record close set a month ago. Despite improving economic data, including a narrowing of the trade gap reported earlier on Tuesday, the S&P 500 is facing a technical hurdle as it nears its all-time high.
"We're at resistance and we need something credible to push us through it. The economy has to undergo a transition from a very weak first quarter, and we're waiting for more proof on that," said Harbor Advisory's De Gan.
The Dow Jones industrial average fell 129.53 points or 0.78 percent, to 16,401.02, the S&P 500 lost 16.94 points or 0.9 percent, to 1,867.72 and the Nasdaq Composite dropped 57.296 points or 1.38 percent, to 4,080.759.
AIG shares fell 4.1 percent to $50.54 a day after posting a 27 percent drop in quarterly income. Financials, down 1.4 percent, were the largest decliners among the S&P 500's top ten industry sectors.
Athenahealth shares slumped 13.9 percent to $109.21, a day after hedge fund manager David Einhorn said the company is part of a portfolio of overvalued stocks his Greenlight Capital was betting against.
Office Depot Inc raised its forecast for full-year adjusted operating income and said it would close at least 400 stores in the United States over two years, sending shares up 15.8 percent to $4.83.
Adding to a string of major deals in the healthcare industry, Bayer acquired Merck's consumer care business for $14.2 billion. Merck shares fell 2.6 percent to $57.11.
About 5.9 billion shares changed hands on U.S. exchanges, below the 6.2 billion average over the past five days, according to data from BATS Global Markets.
Slightly more than two issues declined for every one that advanced on the NYSE, and on Nasdaq more than 18 issues fell for every 5 that rose. (Reporting by Rodrigo Campos; Editing by Nick Zieminski)