(Reuters) - Euro zone businesses started the second quarter with healthy growth as a buoyant order book again encouraged them to hire more, a survey showed on Wednesday.

Any sign that the bloc's recovery is gaining traction will be welcomed by the European Central Bank, which embarked on a trillion-euro bond buying stimulus program in March, although the survey did show firms were still cutting prices.

Markit's final composite Purchasing Managers' Index, seen as a good guide to growth, was 53.9 in April, ahead of an earlier flash reading of 53.5 but just behind March's 11-month high of 54.0. A reading above 50 implies growth.

"The fact that the rate of growth failed to gain further momentum is a disappointment, but the national growth variations will give policymakers some real encouragement that the economic health of the region is improving," said Chris Williamson, Markit's chief economist.

The PMIs suggest quarter-on-quarter growth of 0.4 percent for April-June, Williamson said, which would match forecasts for first-quarter growth.

But to drive that growth firms cut prices again - albeit less sharply in April. The composite output price index, which rose to 49.2 from 48.9, has now been below 50 for three years.

Official data last week showed the euro zone ended four months of deflation in March with consumer prices unchanged from year-ago levels.

Price discounting helped a PMI covering the dominant service industry remain elevated. It came in at 54.1, just shy of March's eight-month high of 54.2 but ahead of the flash 53.7 estimate.

The pace of new orders matched March's near four-year high of 54.6. That encouraged service firms to increase staffing levels for a sixth month.