* ISM services report strong, but ADP report weak
* Many investors worry about low volume and volatility
* Protective Life jumps, Dai-ichi to buy
* NQ Mobile has biggest gain ever, up 28 pct
* Dow down 0.2 pct, S&P down 0.1 pct, Nasdaq up 0.1 pct
(Updates to open, adds ISM data)
NEW YORK, June 4 (Reuters) - U.S. stocks were largely flat on Wednesday as mixed reads on the economy gave the market little direction and traders were reluctant to buy with indexes near record levels.
Wall Street initially opened lower, pressured by a disappointing read on the labor market, but it subsequently cut its losses on a bullish read on the services sector. Trading volume continued to be light, making the market more susceptible to intraday swings and suggesting that recent gains lacked conviction.
The Institute for Supply Management's non-manufacturing index accelerated more than expected in May, rising at the fastest pace in nine months. Separately, fewer private sector jobs were added in May than had been anticipated, according to the ADP National Employment Report.
"With some data strong and other data weak, we don't have a clear picture of the market or the economy right now," said Adam Sarhan, chief executive of Sarhan Capital in New York. "We don't seem to be strong enough to grow without help from the Federal Reserve, but we do seem to be trending in the right direction."
While economic reports have largely been positive lately, investors are concerned about any data that could indicate weakness in Friday's May jobs report.
The Dow Jones industrial average fell 28.72 points or 0.17 percent, to 16,693.62, the S&P 500 lost 1.1 points or 0.06 percent, to 1,923.14 and the Nasdaq Composite added 4.57 points or 0.11 percent, to 4,238.65.
Equities have been strong lately, with the S&P up for seven of the past nine sessions, hitting multiple records.
The CBOE Volatility index was up 2.2 percent, its third straight daily advance. Despite that, the "fear index" remains around 12, well below the historical average of 20, which has some investors concerned the market has become complacent.
In company news, Protective Life jumped 18 percent to $69.25 in heavy trading after Japan's Dai-ichi Life Insurance Co agreed to buy the company for $5.7 billion.
Tibco Software Inc was one of the Nasdaq's most active, slumping 8.2 percent to $19.10 a day after a second-quarter outlook sharply below expectations.
NQ Mobile Inc soared 28 percent to $9.80, its biggest one-day advance ever, moving on heavy volume after the mobile security software maker said a special committee had found no evidence of fraud, as had been alleged by short-seller Muddy Waters Research Group.
(Editing by Bernadette Baum and Nick Zieminski)