The officials want information and reassurances from the company within 24 hours.
"As the days pass with no direct communications from Anthem, our offices are receiving more and more communications from constituents expressing greater and greater frustration," wrote Connecticut Attorney General George Jepsen in a letter Tuesday to Anthem CEO Joseph Swedish.
The hack could have exposed the personal information of as many as 80 million people, if not more, Jepsen said.
He said he was writing the letter on behalf of himself and the attorneys general of Arkansas, Illinois, Kentucky, Maine, Mississippi, Nebraska, Nevada, Pennsylvania, and Rhode Island.
One of the largest U.S. health insurers, Anthem said last week one of its IT systems was breached, resulting in the loss of customer and employee information including income data.
The company said its initial investigation indicated that the data accessed included names, dates of birth, member IDs, Social Security numbers, addresses, phone numbers, email addresses and employment information.
It set up a special website to provide information on the breach, and promised to individually notify current and former members whose information had been accessed. In a statement on the site, Swedish promised to provide credit monitoring and identity protection services free of charge "so that those who have been affected can have peace of mind."
The company said in its FAQ on the site that it continued to work to identify the members who were impacted and would mail letters to those affected in the coming weeks.
Jepsen and the other attorneys general are, however, concerned "at the failure of the company to communicate with affected individuals and, in particular, to provide them details about the protections the company will make available and how to access those protections."
The company assured Jepsen and others last week that free credit monitoring and identity theft protections would be offered to those impacted by the breach, according to the letter. "Since that date, however, few follow-up details have been made available, and none at all about how individuals can sign up for the protections Anthem will provide them," he wrote.
The attorneys general want Anthem to commit to reimbursing consumers for losses from the hack for the period between the breach and the date that the company provides access to credit and identity theft safeguards.
Jepsen has asked Swedish to contact his office on Wednesday to inform him on Anthem's plans to provide protection to its customers.
The company could not be immediately reached for comment.
On Friday, it warned about scam email campaigns targeting current and former Anthem members.