WASHINGTON, July 1 (Reuters) - U.S. manufacturing contracted for a third straight month in June and a measure of prices paid by factories for inputs dropped to a six-month low amid weak demand for goods, indicating that inflation could continue to subside.

The Institute for Supply Management (ISM) said on Monday that its manufacturing PMI slipped to 48.5 last month from 48.7 in May. A PMI reading above 50 indicates growth in the manufacturing sector, which accounts for 10.3% of the economy.

Economists polled by Reuters had forecast the PMI climbing to 49.1. Manufacturing is being pressured by higher interest rates and softening demand for goods.

Government data last week showed manufacturing contracted at a 4.3% annualized rate in the first quarter, with most of the decline coming from long-lasting manufactured goods.

The Federal Reserve has maintained its benchmark overnight interest rate in the current 5.25%-5.50% range since last July. Financial markets expect the U.S. central bank to start its easing cycle in September, though policymakers recently adopted a more hawkish outlook. The Fed has hiked its policy rate by 525 basis points since 2022 to quell inflation.

The ISM survey's forward-looking new orders sub-index rose to a still-subdued 49.3 reading from 45.4 in May. Output at factories decreased for the first time since February. The production sub-index fell to 48.5 from 50.2 in May.

Against the backdrop of weak orders, inflation at the factory gate was much cooler last month. The survey's measure of prices paid by manufacturers dropped to 52.1, the lowest reading since December, from 57.0 in May.

Declining goods prices accounted for much of the unchanged reading in monthly inflation in May. The decrease in input prices last month bodes well for the continued disinflationary trend in the broader economy.

The survey's measure of supplier deliveries rose to 49.8 from 48.9 in May. A reading below 50 indicates faster deliveries.

Factory employment slipped after briefly rebounding in May. Factories are reducing head counts through layoffs, attrition and hiring freezes.

The overall labor market is gradually cooling. The government is likely to report on Friday that nonfarm payrolls increased by 195,000 jobs in June after surging 272,000 in May, according to a Reuters survey of economists. The unemployment is forecast unchanged at 4.0%. (Reporting by Lucia Mutikani; Editing by Chizu Nomiyama)