WASHINGTON, July 6 (Reuters) - U.S. services sector activity dipped in June as some of the boost from businesses rushing to place orders amid the Middle East war ebbed, but employment rebounded after contracting for three straight months, pointing to continued labor market stability.

The Institute for Supply Management said on Monday its nonmanufacturing purchasing managers index edged down to 54.0 last month from 54.5 in May. A reading above 50 indicates growth in the services sector, which accounts for more than two-thirds of U.S. economic activity.

The survey measure of new orders received by services businesses dropped to 55.1 after surging to 57.3 in May. Order backlogs, however, increased last month. 

A similar dynamic was observed in the ISM's manufacturing survey last week. The four-month U.S.-Israeli conflict with Iran raised prices of commodities, including oil. Washington and Tehran have since agreed to a ceasefire, with the fragile truce last month pushing oil prices back to pre-war levels.

The decline in oil prices helped to slow the pace of increase in services inflation. A measure of prices paid by services businesses dropped to a still-high 67.7 from 71.3 in May. Economists have warned that underlying inflation could remain elevated even if oil prices dropped. Businesses are investing heavily in artificial intelligence, driving up prices of goods like semiconductors and electronics.

DELIVERY TIMES REMAIN LONG

Suppliers were still taking longer to deliver inputs to businesses in June. The survey's measure of supplier deliveries eased to a still-elevated 54.4 from 55.2 in May. A reading above 50 indicates slower deliveries. The high reading likely contributed to the small drop in the services PMI as longer delivery times are usually associated with a strengthening economy. In this instance, though, strained supply chains do not reflect strong demand.

The Atlanta Federal Reserve's model is estimating gross domestic product increasing at a 1.2% annualized rate in the second quarter, partly reflecting what so far appears to be a wider goods trade deficit. The economy grew at a 2.1% pace in the January-March quarter, though consumer spending nearly stalled.

Most economists continued to expect that the Federal Reserve would hike interest rates this year, despite job growth slowing considerably in June and revisions showing nonfarm payroll gains in the prior two months were not as strong as previously reported. 

The ISM survey, however, strengthened economists' views that the labor market remained in a "low hire, low fire" state. The survey's measure of services sector employment increased to 51.2 from 47.9 in May. 

The U.S. central bank last month left its benchmark overnight interest rate in the 3.50%-3.75% range, but updated quarterly projections showed policymakers expected to raise borrowing costs this year.