WASHINGTON  Hospitals and insurance companies said Thursday that President Obama had substantially overstated their promise earlier this week to reduce the growth of health spending.

Mr. Obama invited health industry leaders to the White House on Monday to trumpet their cost-control commitments. But three days later, confusion swirled in Washington as the companies’ trade associations raced to tamp down angst among members around the country.

After meeting with six major health care organizations, Mr. Obama hailed their cost-cutting promise as historic.

“These groups are voluntarily coming together to make an unprecedented commitment,” Mr. Obama said. “Over the next 10 years, from 2010 to 2019, they are pledging to cut the rate of growth of national health care spending by 1.5 percentage points each year  an amount that’s equal to over $2 trillion.”