By Sumanta Dey

(Reuters) - Euro zone business growth held steady in June, underpinned by new business and employment, but the modest

pace suggested growth in the second quarter was half the rate of January-March.

Markit's final composite Purchasing Managers' Index for the euro zone was 53.1 in June, beating a flash estimate of 52.8, but unchanged from May. It has been above the 50 mark that divides growth from contraction since mid-2013.

The majority of the survey was completed before Britain voted to leave the EU on June 23, meaning the after-shocks of the referendum have yet to be reflected in the data.

"The survey is signaling GDP (gross domestic product) growth of just 0.3 percent, similar to the sluggish trend recorded over the past year," said Chris Williamson, chief economist at survey compiler Markit.

Euro zone GDP expanded 0.6 percent in the first quarter.

While a late rise in new business, the sub-index for which climbed to 52.8 from a flash reading of 52.5, helped boost overall activity, the pace was still modest and several index points lower than levels seen towards the end of last year.

"The lack of any sign that the upturn is picking up speed will worry policymakers, especially as 'Brexit' uncertainty looks likely to subdue growth in coming months," Williamson said.

The survey showed companies once again cut prices in June in an effort to drum up new business. The output prices index fell to 49.1 from 49.3 in May.

That is likely to disappoint the European Central Bank, which after years of ultra-loose monetary policy, has failed to boost inflation anywhere close to its 2 percent target ceiling.

The euro zone just escaped deflation in June for the first time in five months, with prices up 0.1 percent on a year ago.

The price discounting, however, failed to improve the bloc's dominant service industry. The services PMI fell to 52.8 in June, its lowest since January 2015, from 53.3.

One silver lining in the survey was employment in services firms, which picked up pace in May, pushing that index up to 53.1 from 52.3. Barring a similar reading in December last year, it was the highest since November 2010.

"Although unspectacular, the steady growth of business activity in recent months has given increasing numbers of firms confidence to take on more staff, especially in Germany, Spain and Italy," said Williamson.

((Editing by Hugh Lawson))