The U.S. factory sector shrank further in April but at a slower pace, suggesting some stabilization in the battered sector and the broader economy, according to an industry report released on Friday.

The report hinted at broad improvement in the manufacturing industries, despite the struggles in the U.S. car industry. Chrysler LLC filed for bankruptcy on Thursday and entered into an alliance with Italian carmaker Fiat.

The Institute for Supply Management said its index of national factory activity rose to 40.1 in April from 36.3 in March. The median forecast among economists polled by Reuters was 38.0.

A reading below 50 indicates contraction in the manufacturing sector. ISM said the index has been below this threshold for 15 straight months, but it has been rising for four consecutive months.

If the ISM manufacturing index hits 44 by this summer, it could mean a stop in the shrinking in the overall economy, according to Ian Shepherdson, chief U.S. economist at High Frequency Economics.

That's immensely significant, because 44 is consistent with stable GDP, Shepherdson wrote in a research note.

The report's new orders index jumped to 47.2 in April, the highest since August 2008, from 41.2 in March.

Increased orders could mean fewer factory layoffs. The employment component rose to 34.4 in April, its best showing since September, from 28.1 in March.

(Reporting by Richard Leong, Editing by Chizu Nomiyama)