WASHINGTON — U.S. factory activity grew at a slower pace in June for the third straight month as measures of new orders and inventories fell.

The Institute for Supply Management, an association of purchasing managers, said Monday that its manufacturing index slipped to 51.7 last month from 52.1 in May. Any reading above 50 signals an expansion.

While the sector is still growing, the report pointed to an ongoing weakening in U.S. manufacturing. Trade fights with China, Europe and Mexico, as well as an increase in the dollar’s value, have cut into U.S. exports and increased uncertainty for American manufacturers.

A measure of new orders dropped to 50, which means they were unchanged. Manufacturers are also holding fewer supplies, a sign they are worried that demand could slow further.

“It’s concerning,” said Tim Fiore, chair of the ISM’s manufacturing survey committee. “This is going down faster than I would like.”

The ISM surveys purchasing managers at manufacturing firms, nearly half of whom said that trade policy was negatively affecting their businesses.

“Tariffs are causing an increase in the cost of goods, meaning U.S. consumers are paying more for products,” a chemical manufacturer told the ISM.

A measure of new export orders was just 50.5, suggesting overseas demand is barely growing. Overall order backlogs are also shrinking, and customers’ inventories, while still declining, are doing so more slowly. When customers hold larger stockpiles, that means they order fewer goods from factories.

There were positive signs: Production and employment increased at a faster pace in June.