A spokeswoman for CGI, Linda Odorisio, didn’t respond to an e-mail seeking comment on the decision. Joanne Veto, an Accenture spokeswoman, declined to comment, saying the company is always in contact with prospective clients.

CGI declined 3.9 percent to $31.23 at 1:31 p.m. New York time. Accenture dropped less than 1 percent to $82.74.

Diminished role

The government-run insurance exchanges offer health plans and access to subsidies created by the 2010 Patient Protection and Affordable Care Act. CGI’s role in managing healthcare.gov had been reduced following the botched rollout, with a unit of UnitedHealth Group Inc. brought in to oversee emergency repairs. Most Americans have until March 31 to select a health plan for 2014 coverage.

The government had spent $319 million building healthcare.gov and its supporting technology as of Oct. 31, according to Albright’s agency. Marilyn Tavenner, the CMS administrator, and Kathleen Sebelius, the U.S. health secretary, each told Congress in hearings late last year that CGI had failed to meet expectations under its contract.

Accenture would be a good fit to take over the contract because of its reputation and size, said David Grossman, an analyst at Stifel Nicolaus & Co.

‘Best’ in business

“They would have both the scale and the resources to bring to bear to improve this system, get it working and then support it,” he said in a phone interview. “A lot of the risks and the issues are already known, and the government is in a bad spot. Given how important this is to the current administration, I think you would want to get somebody who is the best in the business to try to fix it.”

In addition to the federal site, CGI built health exchanges for Massachusetts and Vermont, which have also criticized the company’s work.

Vermont on Nov. 21 told CGI that it would dispute $1.1 million in charges for the company’s work on its Health Connect exchange and deduct $5.1 million in damages from the state’s payments to the firm. Leaders of the Massachusetts Health Connector told their board of directors yesterday that most people applying for insurance at the state’s exchange haven’t been able to use its website because of CGI’s poor performance.

“Incomplete and inadequate IT functionality as a result of an under-performing vendor has made it difficult for users to complete the application process,” the exchange’s staff said in a presentation. Governor Deval Patrick, a Democrat, instructed the exchange “to consider all of our legal rights related to CGI’s failure to perform and the cost of remediation,” according to the presentation.

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