HCA Inc., the nation's largest for-profit hospital chain, said yesterday that it would pay the federal government $631 million more to settle fraud claims, bringing the results of a long-running Justice Department investigation of the company to a record $1.7 billion.

The agreement, which still must be approved by department officials, signals the likely end to a probe of allegations, aided by a series of whistle-blowers, that the company systematically overcharged Medicare and other public insurance programs. It comes just two years after the health care industry giant, formerly known as Columbia/HCA Healthcare Corp., agreed to pay the government $840 million to settle criminal and civil charges that it defrauded Medicare. It also agreed to plead guilty to paying kickbacks to doctors to steer patients to its facilities.

HCA chairman and chief executive Jack O. Bovender Jr. said he hoped that the settlement will close out a sordid chapter of the company's history. The company has taken steps to ensure it has "corporate integrity," he noted, and a "culture that is focused on the delivery of quality patient care in the communities we serve." Shares of HCA closed at $42.90, up 3.4 percent after the announcement.

"We are pleased to have successfully negotiated a settlement," Bovender said. "Today, we are a stronger company."

The False Claims Act, which permits whistle-blowers to make health care fraud claims and pursue litigation on the government's behalf in exchange for a share of the settlements, played a key role in the case. The department joined several private suits brought by former HCA employees.

"This is the end, really, of a 10-year odyssey," said John R. Phillips, of Phillips & Cohen LLP in the District, who helped lead a massive private probe into the hospital chain's practices on behalf of two clients who first filed allegations of fraud in 1993.

Yesterday's agreement settles civil allegations the Justice Department brought last year, joining several whistle-blower cases, about the alleged kickbacks to physicians and about "cost reports" -- reimbursement reports the company sent to Medicare, Medicaid and other federal health care programs for services, capital expenses, janitorial work and the management of HCA's wound-care facilities.

Under the agreement, HCA would pay $631 million to settle those allegations; that is on top of $250 million it agreed to pay in March to resolve "outstanding cost report issues" with the Centers for Medicare and Medicaid Services, the federal agency that runs Medicare and Medicaid. The company also said it would pay $17.5 million to resolve similar claims by state Medicaid officials.

HCA co-founder Thomas F. Frist Jr. is the brother of Sen. Bill Frist (R-Tenn.). He and Bovender were scheduled to deliver depositions in the case.

The alleged fraud began in the 1980s, when two companies that eventually formed HCA began keeping "what were essentially a secret set of books that detailed reimbursement claims made on cost reports that the companies knew were improper," according to a statement by Phillips & Cohen. Employees were specifically told not to share information from the secret books with government auditors.

After an employee of a Montana hospital that had been managed by a former HCA company was fired for refusing to file questionable cost reports, he filed a lawsuit under the False Claims Act in January 1993. Another employee of a Columbia-affiliated hospital in Florida filed a similar claim in 1996.

In 1997, the FBI conducted a massive raid of the company's facilities nationwide and seized thousands of cost reports. After years of examining the documents, private attorneys and government investigators said they were able to demonstrate that the company engaged in systematic efforts to defraud the government and cover its tracks. The company pleaded guilty to 14 criminal counts two years ago.

At its peak, HCA had some 280 hospitals and other facilities. Now it owns about 180 hospitals and other providers in 23 states, England and Switzerland.

Phillips said the government has not made clear how it came to the final settlement figure or how much his whistle-blower clients will receive. "We may very well object," he said.

Sen. Charles E. Grassley (R-Iowa), the incoming chairman of the Senate Finance Committee and a leading proponent of the False Claims Act, also questioned whether the settlement was large enough.

"The most important question is unanswered. That's whether the taxpayers will get their money back from any fraud perpetrated by HCA," he said in a statement. "Until I see the math, I'll remain skeptical."