But on Wednesday, the White House press secretary, Robert Gibbs, said Mr. Obama had scrapped the idea.
“The president has instructed that its consideration be dropped,” Mr. Gibbs said.
The press secretary said Mr. Obama had heeded the concerns of veterans’ organizations that feared the proposal could make it more difficult for some of their members to obtain care.
In a recent letter to the president, the American Legion and 10 other veterans organizations denounced the proposal as “a total abrogation of our government’s moral and legal responsibility” to treat service-connected injuries and illnesses.
Lawmakers of both parties said the proposal would have made it more difficult for some veterans to get affordable private health insurance for themselves and their families.
“Pushing combat injuries onto personal insurance plans could make service to our nation a pre-existing condition,” which could be used to justify the denial of private coverage, said Representative Roy Blunt, Republican of Missouri.
Mr. Obama has repeatedly called health insurance for all Americans one of his priorities.
Veterans groups thanked the president on Wednesday.
Jay Agg, a spokesman for Amvets, said: “We are very pleased the administration dropped this proposal. It flew in the face of the government’s covenant to care for all service-connected needs of our veterans.”
Glen M. Gardner Jr., national commander of the Veterans of Foreign Wars, said Mr. Obama had told veterans on Monday that he would listen to their concerns. “The president kept to his word and made the right decision,” Mr. Gardner said.
Senior members of Congress had threatened to kill the proposal if Mr. Obama pushed it.
The chairmen of the House and Senate Committees on Veterans Affairs, Senator Daniel K. Akaka, Democrat of Hawaii, and Representative Bob Filner, Democrat of California, had publicly opposed the proposal.
“Our budget cannot be balanced on the backs of our nation’s combat-wounded heroes,” Mr. Filner said.
Speaker Nancy Pelosi, Democrat of California, announced the president’s decision Wednesday afternoon at a meeting with veterans groups. Leaders of the organizations had pressed their concerns a few hours earlier in a meeting at the White House with Rahm Emanuel, the president’s chief of staff.
Eric Shinseki, the secretary of veterans affairs, said Mr. Obama was requesting $113 billion for the department in 2010, an increase of 16 percent over this year’s amount. The budget includes money to treat 419,000 veterans of the Iraq and Afghanistan wars, up 15 percent from this year and 61 percent from 2008.
Having dropped the idea of billing private insurers for the treatment of service-connected conditions, administration officials have told veterans groups that they want to find another way to save a similar amount of money.
One way is to collect payments from private insurers who are already responsible for some care provided to veterans for needs unrelated to their military service.