WASHINGTON, July 6 (Reuters) - U.S. services industry activity grew at a moderate pace in June, likely restrained by labor and raw material shortages, resulting in unfinished work continuing to pile up. The Institute for Supply Management said on Tuesday its non-manufacturing activity index fell to 60.1 last month from 64.0 in May, which was the highest reading in the series" history. A reading above 50 indicates growth in the services sector, which accounts for more than two-thirds of U.S. economic activity. Economists polled by Reuters had forecast the index easing to 63.5. The economy has been hit by shortages of labor and raw materials as it reopens after more than a year of disruptions caused by the COVID-19 pandemic. More than 150 million people are fully immunized against the coronavirus, resulting in the lifting of pandemic-related restrictions on businesses and mask mandates, helping demand to revert back to services from goods. The survey"s measure of backlog orders increased to a reading of 65.8 from 61.1 in May. New orders remained healthy and there is ample scope for hefty gains in the months ahead, with inventories contracting in June. Inventory sentiment among customers remained poor. Business inventories were depleted in the first quarter amid pent-up demand. With supply constraints showing no sign of letting up, businesses continued to pay more for inputs. The survey"s measure of prices paid by services industries dipped to a still-high 79.5 from 80.6 in May, which was the highest reading since September 2005. The continued elevation supports some economists" view that higher inflation to prove to be more persistent than currently envisioned by the Federal Reserve. Fed Chair Jerome Powell has repeatedly stated that higher inflation will be transitory noting that he expected supply chains to normalize and adapt, views also shared by Treasury Secretary Janet Yellen. The Fed"s preferred inflation measure for its 2% target, the personal consumption expenditures price index, excluding the volatile food and energy components, shot up 3.4% year-on-year in May, the largest gain since April 1992. read more The ISM survey"s measure of service employment fell to a reading of 49.3 in June from 55.3 in May. There is, however, cautious optimism that the worker shortage is starting to ease. The government reported on Friday that nonfarm payrolls increased by 850,000 jobs in June, the largest gain in 10 months, after rising 583,000 in May. read more