Massachusetts today extended from March 31 until April 15 the deadline to enroll in health coverage, giving two additional weeks to residents who have been stymied by the state’s faulty health insurance website.

The extension applies to those who do not need subsidized coverage and follows a similar extension granted earlier this week by the Obama administration for residents who have been blocked by the federal health exchange. Those who need subsidized coverage will not face any deadline to enroll, officials said.

At a board meeting of the Massachusetts Health Connector, officials also announced some good news: a backlog of 72,000 paper applications for health insurance coverage, many submitted by low-income residents, has been completely eliminated.

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The backlog had piled up after officials encouraged residents to file paper applications because the state insurance website has been hobbled by error messages since it was revamped in October to comply with the more complex requirements of the federal health care law.

The applications were expected to take months to process, but were done in about six weeks after officials developed a data-entry system that cut from two hours to 27 minutes the time it took for the state to enter each application into a database.

Those residents have now been given temporary health insurance coverage through the state Medicaid program.

Sarah Iselin, a health insurance executive whom Governor Deval Patrick has put in charge of fixing the website, called the end of the backlog a “really, really exciting moment.”

Meanwhile, she acknowledged that officials are still struggling with the larger problem of how to fix the website in time for the next open enrollment period in November.

She said officials are weighing whether to rebuild the existing system, or borrow parts from states like Kentucky that have functioning health insurance exchanges.

Earlier this month, Massachusetts dumped CGI, the contractor that designed the new Massachusetts website and built the federal HealthCare.gov website that got off to a disastrous start last fall, but has since been largely fixed.

Iselin said officials are wrangling with CGI over access to the computer codes for the website and over how much the state owes the firm.

CGI claimed in a March 14 letter to Iselin that it has not received payment since summer 2013, even as it has continued to work on the website.

“We’re in the midst of a negotiation,” Iselin said. “The code is clearly owned by the Commonwealth. But clearly there are a lot of aspects to this negotiation, including the question of what, if anything, in addition to what we’ve already paid CGI, we will pay them as part of the transition, and it’s just too soon to say.”

In its letter, CGI also blamed the state for problems with the website, accusing officials of poor governance, lack of timely decision-making, and of constantly changing the scope of the work.

Iselin declined to comment on those accusations, saying, “I can’t speak to anything that happened before the time that I arrived,” in February.

But she said, “We have a solid governance structure and management structure to ensure we get to a fully functioning website that supports our health insurance exchange.”

The state is currently facing a deadline of June 30 move the 125,000 residents enrolled in temporary Medicaid coverage to plans that comply with the federal health care law. But because the website is not expected to be fully functioning by that date, officials have previously said they plan to ask the Obama administration to extend that deadline until Sept. 30.