State officials are moving to fire CGI, the contractor responsible for Massachusetts’ broken health exchange website, and are starting to search for a new vendor, the state’s Obamacare czar said this morning.

“We have made the decision that we are going to be parting ways with CGI,” Sarah Iselin said. “We have just begun the process of negotiating what we hope will be a very careful transition.”

Iselin said the goal is to have the website working by the fall — a full year after its initial launch. Because of its myriad glitches, the Health Connector has had to enroll people in health coverage through paper applications.

Hundreds of employees at Optum, a technology company hired to manage enrollment problems, have been poring through a backlog of applications, now at 21,000. The backlog was at 72,000 about a month ago.

The federal deadline for enrolling in health plans for 2014 is March 31.

“We think we’re going to be caught up well before the end of the month,” Iselin said. “We don’t expect to fall behind again.”

The state has paid $15 million of a $69 million contract with CGI. Connector officials have not said how much taxpayers will have to pay to fix problems with the health exchange.