The research firm's manufacturing production index for June came to an estimated 53.9, up from May's 52.7 level.
The overall manufacturing picture was little changed with the headline index, the Purchasing Managers Index, sliding one tick to 52.2 in June from 52.3 in May.
The figures are flash estimates, which are based on 85 percent of the expected replies to a survey conducted June 12-19 that includes 5,000 businesses.
Results of the survey above 50 indicated growth while results below 50 indicate a contraction.
The flash estimate for new orders was 53.7, showing faster growth than May, when the new orders index was 53.3.
The employment index, however, showed slower growth, dropping from 52.6 to 50.4. Backlogged orders for work showed marginal growth, climbing from 51.2 to 51.5, Markit said.
"The U.S. manufacturing sector appears to have remained stuck in a low gear in June, rounding off the weakest quarter since the third quarter of last year," Markit Chief Economist Chris Williamson said in a statement.
"With the average PMI reading down to 52.2 [compared to 54.9 in the first three months of the year] slower growth in the goods-producing sector looks likely to have acted as a drag on the wider economy, pulling GDP growth down from the annualized rate of 2.4 percent seen in the first quarter," he said.