WASHINGTON — Thousands of Medicare patients with severe chronic illnesses such as Alzheimer’s would get continuing access to rehab and other services under a change agreed to by the Obama administration, advocates said Tuesday.

The proposed agreement in a national class action suit would allow Medicare patients to keep receiving physical and occupational therapy and other skilled services at home or in a nursing home so they can remain stable, said Gill Deford, a lawyer with the Center for Medicare Advocacy.

That’s been a problem for some because of a longstanding Medicare policy that says patients must show improvement to keep getting rehab. Deford’s group and other organizations representing patients challenged it.

“If you have a chronic condition, by definition you are not improving,” said Deford, the lead attorney on the case. “Our view is that Medicare regulations were intended to allow people to maintain their health status. They don’t have to show they are getting any better. The point is to allow them not to get any worse, if possible.”

The agreement was filed with Chief Judge Christina Reiss of the U.S. District Court in Vermont. It is expected to affect tens of thousands — maybe hundreds of thousands — of patients nationally. Those who stand to benefit include not only people with intractable conditions like Alzheimer’s, multiple sclerosis, Parkinson’s and chronic lung disease. Those who are growing weaker because of advancing age, placing them at greater risk of falls and other problems, could also be helped.

The impact on Medicare’s budget is unclear, partly because program rules are not always rigidly enforced. Even with a requirement that patients must continue to show improvement, billing contractors sometimes defer to the clinical judgment of doctors and therapists. A patient’s underlying disease may be advancing, but therapy might help them keep up strength up and do more to take care of themselves. Still, that’s no guarantee that Medicare will pay.

“That’s what the point of this case is,” said Deford, adding his center has represented many people repeatedly denied coverage for rehabilitation services. “This will allow them to have access.” Advocates say Medicare could break even financially, if patients don’t have to go to the hospital.