WASHINGTON, April 11 (Reuters) - The U.S. Cybersecurity and Infrastructure Security Agency said Russian government-backed hackers have used their access to Microsoft's email system to steal correspondence between officials and the tech giant, an emergency directive by the U.S. watchdog released on Thursday showed.

In the directive dated April 2, the agency warned that hackers were exploiting authentication details shared by email to try to break into Microsoft's customer systems, including those of an unspecified number of government agencies.

CISA declined to name agencies that might have been affected. Microsoft did not immediately respond to a message seeking comment.

"Other organizations may also have been impacted by the exfiltration of Microsoft corporate email," CISA said, encouraging customers to contact Microsoft for further details.

(Reporting by Raphael Satter; Editing by Franklin Paul and Richard Chang)