By ROBERT PEAR

ASHINGTON, June 6 — Representative Charlie Norwood, a leader of the six-year campaign for legislation defining patients' rights, said today that the White House had expressed a new willingness to support a compromise letting patients sue health insurers for medical injuries caused by substandard care.

Mr. Norwood said he and the White House favored the proposal, which would allow patients to recover up to $4 million for pain and suffering and other noneconomic damages resulting from serious injuries.

"This is the best deal Congress will get," Mr. Norwood said, expressing hope that the idea would open the way to final approval of the legislation.

The Senate, defying a veto threat from President Bush, passed a patients' bill of rights 59 to 36 last June. The House passed a different version, with a much more limited right to sue, last August by a vote of 226 to 203. Mr. Bush supported the House bill.

Under the Senate bill most cases would go to state courts, subject to any limits of state law, while the House bill would limit pain and suffering to $1.5 million.

The White House and several senators have engaged in quiet negotiations for months, especially over the legal liability of health maintenance organizations and other insurers.

Mr. Norwood, Republican of Georgia, said the negotiators had made significant progress on all other issues, and the White House confirmed that.

"Both sides have come a million miles," Mr. Norwood said. "They are down to the last inch."

In an interview, Mr. Norwood said White House officials had assured him they would accept a $4 million cap on damages for serious injuries.

"Most everybody is willing to go along with this deal except a few people in Congress," he said.

A White House spokesman confirmed the discussions but declined to be more specific.

Mr. Norwood said Senator John McCain, Republican of Arizona and the chief sponsor of the Senate bill, which would give patients broad new rights to sue, has seen the proposal. The two Democratic sponsors of the Senate measure, Edward M. Kennedy of Massachusetts and John Edwards of North Carolina, have not accepted the idea of a $4 million cap, and many plaintiffs' lawyers oppose any limit on damages as unfair to patients.

Frustrated with the pace of negotiations, Mr. Norwood asked, "What is this fight about? Many states already have caps lower than $4 million. The average jury verdict and the average out-of-court settlement in medical injury cases are much less than $4 million."

Senator Kennedy has been tight-lipped about the negotiations, indicating that he was more interested in enacting legislation than in scoring political points.

"While I remain hopeful that we can reach an agreement that fully protects all patients from H.M.O. abuse," Mr. Kennedy said tonight, "we are well into the ninth inning, and time is running out on our discussions."

Scott McClellan, a White House spokesman; Nancy E. Ives, a spokeswoman for Mr. McCain; and James P. Manley, a spokesman for Mr. Kennedy, would not discuss details of any proposal.

Mr. McClellan said the White House has been working to reach a bipartisan consensus.

"We believe it was within reach, and could still be," he said. "The real question now is whether the interests of powerful personal injury trial lawyers will prevail over the health care needs of the American people."

The White House and Senate negotiators said they had discussed proposals that would set different limits on lawsuits for serious injuries and other, less severe injuries. Under the proposal described by Mr. Norwood, the limit would be $1.5 million for less serious injuries.

For serious and less serious injuries, Mr. Norwood said, there would be a $1.5 million cap on punitive damages but no limit on economic damages, which reimburse patients for medical expenses and lost wages.

Lawmakers said they had not reached agreement with the White House on how to define the difference between more serious and less serious injuries.

If negotiations with the White House fail, Congress could appoint a conference committee, the usual mechanism for resolving major differences between the House and the Senate.

Supporters of the legislation have been trying to avoid a conference committee. An earlier version of the patients' rights bill died in such a committee in 2000, after countless hours of negotiations that frustrated members of both parties.

Tom Daschle, Democrat of South Dakota, the Senate majority leader, said on Wednesday that he was close to seeking a conference committee because of "the intransigence that we have had from the Republicans and the White House."

"We're getting very mixed signals," Mr. Daschle said, "and I don't know that the White House wants to press ahead. They don't appear to want an agreement, and we're left with really no choice, it seems, but to appoint conferees."