(CNN) —  

Defense Secretary Ash Carter says the military is “looking into” service members’ use of the website Ashley Madison after more than 15,000 government-connected email accounts were included in the personal details published by hackers.

“Of course it’s an issue because conduct is very important,” Carter said at a Thursday afternoon news conference.

“We expect good conduct on the part of our people,” he said, adding that “the services are looking into it and as well they should be – absolutely.”

Carter is the first high-ranking official in President Barack Obama’s administration to weigh in on the hack of the website, which advertises itself as a place for married people to connect in order to have affairs.

The hackers this week released personal details – including names, email addresses and credit card information – for more than 32 million people who were registered for the site.