President Carter renewed his battle for hospital cost control legislation yesterday, billing it as part of his war on inflation, a war he called "of equal importance" to his drive for Middle East peace.

"I know" the bill will not be passed "without a difficult fight," he said, nothing that a similar bill was defeated last year by the hard work and hard spending of hospital and medical organizations.

"I will lead the fight on behelf of the American people," he promised as he sent a new version -- more compromising in some ways, tougher in others -- to Capitol Hill.

"The hospital lobby defeated it last year," the president said. "It's more determined and well-financed this year, but the patience of the American people is wearing thin, and rightly so."

Members of Congress and Hill aides on both sides of the issue agreed yesterday that "the mood is different this year," as one said. and the bill has at least a fighting chance.

"I think we're going to win," Rep. Henry A. Waxman (D-Calif.), new chairman of the House Commerce health subcommittee, told Carter at a White House news briefing. The briefing -- in a Cabinet Room packed with reporters, cameras and eight key senators and representativs and their aides -- was one step among many in the new, high-priority fight to put a federal limit on hospital prices, should the hospitals' own efforts fail.

But a more powerful legislator, Sen. Herman E. Talmadge (D-Ga.), merely told the president, "I think you covered the issue very well. I have nothing to add."

Talmadge heads the Senate Finance Committeehs health subcommittee, and he has his own, milder hospital cost control bill. It would affect only federal Medicare-Medicaid payment and cut far less deeply into hospital revenues.

Talmadge and Senate Finance Chairman Russell B. Long (D-La.) have refused to co-sponsor the administration bill, a White House aide said. The president was backed by all the other legislators present: Sens. Edward M. Kennedy (D-Mass.), Senate Human Resources health subcommittee head; Gaylord Nelson (D-Wis.), author of a successful, last-ditch effort to get a bill through the Senate last year; Harrison A. Williams (D-N.J.) and Jacob K. Javits (R-N.Y.), and Reps. Harley Staggers (D-W.Va.), who failed to get a measure through his full Dommerce Committee last year, and Charles B. Rangel (D-N.Y.), new head of the House Ways and Means health subcommittee.

The strategy this year calls for Kennedy to open Senate eharings Friday, and Rangel and Waxman jointly on Monday. Then Rangel will try to steer the bill through his subcommittee and the full Ways and Means Committee, on the theory that these bodies -- though far from known quantities on this issue -- will be easier on it than Waxman's subcommittee. That body has a more conservative cast that last year.

With many exceptions -- measures to try to win hospital support -- the administration bill would slap a federal price lid on hospitals that fail to limit 1979 spending to a figure 9.7 percent above 1978's.