The most recent incident came in the week starting Sept. 15, before a security upgrade, the officials said. Iranian officials didn’t respond to requests to comment.

The allegations would mark one of the most serious infiltrations of U.S. government computer systems by Iran. Previously, Iranian-backed infiltration and surveillance efforts have targeted U.S. banks and computer networks running energy companies, current and former U.S. officials have said.

In the Navy’s case, the Iranian intruders penetrated an unclassified computer network that is used for email and the service’s internal intranet, the officials said.

The U.S. officials said they didn’t believe Iranian agents stole information of significant value, but the incident sparked concerns within the Pentagon because it showed a more potent Iranian hacking capability than previously believed and suggested the Iranians have the ability to access military data.