Under pressure from inmate advocates and with legislative support evaporating, Mayor Vincent C. Gray on Tuesday backed off a plan to award a $66.1 million contract for health care at the D.C. jail to a controversial Tennessee firm.

City procurement officials had tentatively awarded the three-year contract last month to Corizon Health Inc. — the nation’s largest provider of health care in prisons and jails, operating in more than 500 facilities in 27 states. The D.C. Council was set to vote on the contract Wednesday.

But Gray (D) withdrew the contract Tuesday evening, according to D.C. Council Chairman Phil Mendelson (D) and an administration official, who both said it appeared that Corizon did not have enough support for approval.

Critics say the company’s track record, as documented in litigation and news reports, make it a poor choice for the city’s roughly 2,000 inmates — particularly because it would displace Unity Health Care, the local nonprofit group that has run a highly regarded program aimed at coordinating health care for inmates after they leave the jail.

Deborah M. Golden, who directs the D.C. jail program for the Washington Lawyers’ Committee for Civil Rights and Urban Affairs, said that Corizon has been responsible for a “parade of horrors” in other jurisdictions.

“That’s not the care we need in D.C.,” Golden said. “We need a community-based model that has roots in the city with the ability to have seamless follow-up with people in and out of the jail.”

But Corizon and city officials are asking lawmakers to respect a procurement process that stretched over 18 months and involved seven rounds of bidding. The final bidding rounds involved just two firms: Corizon and Unity.

According to a summary of the procurement submitted to the D.C. Council, Corizon provided positive evaluations of its performance from other jurisdictions and subcontracted to a local firm its mental-health services. Its bid, according to the summary, was priced 7 percent higher than Unity’s but had a “significant technical advantage.”

“I’m very satisfied that there was a very thorough and comprehensive evaluation that went into this,” said Thomas Faust, head of the Department of Corrections. “What’s the point of having such a thorough and complete process and then ignoring that process?”

Corizon spokeswoman Courtney Eller said in a statement that the award was made “based on our technical expertise, pricing for our evidence-based clinical programs and services, and the outstanding 35-year track record of the company.” More than half of the privately held firm’s clients, she said, have been doing business with Corizon for at least a decade.

Gray’s withdrawal of the contract does not necessarily block the award. Mayor-elect Muriel E. Bowser (D) could resubmit the contract after she takes office Jan. 2. Or, she could move to start a new procurement. Faust said that if the contract is not approved, Unity would remain in place for the rest of the fiscal year, costing the city nearly $2 million in savings it would reap under Corizon.

But opponents of the Corizon award say that approving the contract — which could be extended to five years and more than $100 million — would be penny-wise and pound-foolish, citing the risk of litigation.

Three states that have employed Corizon — Arizona, Alabama and Virginia — have been the targets of recent wide-ranging civil rights lawsuits alleging that patient care had become secondary to financial concerns.

Arizona moved to settle a class-action brought by the American Civil Liberties Union in October, agreeing to address chronic understaffing; Virginia also moved last month to settle a class-action case, filed by the Legal Aid Justice Center on behalf of inmates of the Fluvanna Correctional Center for Women. Alabama continues to fight a suit filed in June by the Southern Poverty Law Center alleging inadequate care.

The litigation, as well as suits by individual inmates in various jurisdictions who say that Corizon did not adequately treat their illnesses and injuries, has fueled the opposition — from groups including the ACLU, University Legal Services and the union representing corrections officers.

Eller said the Arizona lawsuit pertained to conditions that existed before Corizon contracted with the state, adding, “In our litigious society, people file lawsuits for many reasons of their own” — most of which, she said, are dismissed or settled.

The critics won backing from several lawmakers, including Mendelson, who cited Corizon’s “reputation for attracting a lot of lawsuits” in discussing his opposition Tuesday.

Before Unity started working in the jail in 2006, Mendelson said, “the city suffered huge, huge losses from lawsuits as a result of health care. . . . And over the last eight years, the number of lawsuits against the District and the value of the lawsuits have just plummeted. And that’s a good thing.”

In recent days, Unity, the operator of a network of clinics serving low-income city residents, had urged council members to overturn the contract. “For eight years, we have implemented a model that has been both nationally and locally recognized,” said Vincent A. Keane, Unity’s president and chief executive. “Why did the District, after eight years of success, abandon this model?”