The rate at which U.S. manufacturing grew in June was slightly less than the rate at which it grew in May, private economic data firm Markit reported Monday, and weakening exports were a big factor.

Markit's purchasing managers' index for last month came in at 51.9, down slightly from May's 52.2 and less than the 52.3 many analysts had expected.

The growth in the U.S. factory sector has slowed to an eight-month low, Markit said.

“Manufacturing clearly downshifted a gear between the first and second quarters, and it is at risk of losing further momentum as we head into the second half of the year," said Chris Williamson, Markit's chief economist.

"Output growth remained well down on the robust pace seen at the start of the year and persistent weak order book growth suggests the sector is at risk of stalling. Domestic demand is far from lively, but it is a deteriorating export scene that is causing the real problem. Export orders are being lost at the fastest rate since the height of the financial crisis in mid-2009,” Williamson said.