“We are committed to working together to bend the health care cost curve,” the groups said in a joint statement. “We are committed to doing our part to make reform sustainable and to make the system more affordable and effective for patients and purchasers.”

The statement followed news reports detailing doubts raised this week by the American Hospital Association and the Advanced Medical Technology Association about the agreement to trim $2 trillion from health care spending over the next decade.

Hospital association President Richard Umbdenstock told his members in a conference call Thursday that the deal has been “spun way away from the original intent,” and that the association did not agree to reduce the spending rate by 1.5 percentage points annually — as President Barack Obama had said — but, rather, over 10 years.

Also, an executive with AdvaMed told The New York Times that “there was no specific understanding” of when the lower growth rate would be achieved.

POLITICO reported Friday that officials familiar with the process said the White House publicized the deal before it was ready. The White House outlined the agreement to reporters on Sunday, but it could not provide specific details on what the groups had agreed to trim.

Obama announced the deal Monday, and the groups released a letter stating they would meet the administration’s “goal of decreasing by 1.5 percentage points the annual health care spending growth rate — saving $2 trillion or more.”

White House Budget Director Peter Orszag took to his blog Friday to dispute the notion of a misunderstanding, although he did acknowledge the groups “have since clarified that they may need to ‘ramp up’ to the 1.5 percentage point reduction in the growth rate, which is understandable.”

“Allowing some time for a ramp-up does not change the fundamental point,” Orszag wrote in a post titled “Misdiagnosis.” “The groups have committed to significant reductions in the growth rate, thereby recognizing that substantial efficiencies can be captured in the health system. Some ramp-up time also does not materially affect the long-term impact from reducing the growth rate, on either national health expenditures or the Federal budget.”

The six organizations with a major stake in health care reform — the Service Employees International Union, the American Medical Association, America’s Health Insurance Plan, the Pharmaceutical Research and Manufacturers Association, the AHA and AdvaMed — had been working in secret for several weeks on a savings plan.

And they continue to meet in an effort to present a more detailed plan to Obama by June 1.

“Our organizations are currently engaged in an intensive process to develop proposals to reduce the rate of increase in future health care costs,” the groups said in the joint statement. “And to be successful, we must take action in public-private partnership. We look forward to offering cost-savings recommendations in the weeks ahead.”