WASHINGTON, June 3 (Reuters) - A measure of U.S. services industry activity increased to a record high in May amid robust demand as the economy moves toward fully reopening, but businesses are struggling to source raw materials and labor, driving up production costs. The Institute for Supply Management (ISM) said on Thursday its non-manufacturing activity index rebounded to 64 last month, the highest reading in the series’ history, from 62.7 in April. 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 climbing to 63.0. The rise in the services industry index partly reflected a jump in the survey’s measure of supplier deliveries to a reading of 70.4 from 66.1 in April. A reading above 50 indicates slower deliveries. A lengthening in suppliers’ delivery times is usually associated with a strong economy and increased customer demand, which is a positive contribution to the index. Pent-up demand is being unleashed as the COVID-19 pandemic’s grip slackens because of vaccinations, allowing authorities to lift restrictions on businesses. But the boom in demand is running into supply constraints, leading to a piling up of unfinished work. The survey’s measure of backlog orders soared to a reading of 61.1 from 55.7 in April. That mirrored the findings of the ISM’s manufacturing survey published on Tuesday. With the bottlenecks in the supply chain showing no sign of easing, businesses paid more for inputs. The survey’s measure of prices paid by services industries shot up to 80.6, the highest reading since September 2005, from 76.8 in April. That could strengthen the argument among some economists that higher inflation could last longer rather than being transitory as currently envisioned by Federal Reserve Chair Jerome Powell. The government reported last Friday that a measure of underlying inflation tracked by the Fed for its 2% target accelerated 3.1% on a year-on-year basis in April, the largest increase since July 1992. The ISM survey’s measure of new orders for the services industry edged up to a reading of 63.9 from 63.2 in April. Businesses appeared to have hired fewer workers last month, likely because of labor and raw material shortages. Workers are scarce despite nearly 10 million Americans being officially unemployed. Generous unemployment benefits funded by the government, problems with child care and fears of contracting the virus, even with vaccines widely accessible, as well as pandemic-related retirements have been blamed for keeping workers home. The survey’s measure of services industry employment dropped to 55.3 from a reading of 58.8 in April. That, together with a moderation in employment gains at factories last month, could temper expectations for an acceleration in job growth in May after nonfarm payrolls increased by only 266,000 in April. According to a Reuters survey of economists, payrolls likely increased by 650,000 jobs last month. The Labor Department is scheduled to publish May’s employment report on Friday. (Reporting by Lucia Mutikani Editing by Chizu Nomiyama) Our Standards: The Thomson Reuters Trust Principles.