CareFirst BlueCross Blue­Shield, the largest private insurer in the Washington region, said Thursday that an experimental program that rewards doctors for coordinating care of their sickest patients resulted in better care and savings of nearly $40 million last year.

The program, part of the health-care overhaul, is one of the largest among dozens of public and private experiments testing this approach. Known as the patient-centered medical home model, it rewards teams of doctors, nurses and other staff members for coordinating care of patients with multiple chronic diseases. The goal is better care for patients, as well as lower costs because of fewer emergency visits and hospital stays.

About 3,600 primary-care doctors and nurse practitioners are taking part in the CareFirst program, or about 80 percent of those actively practicing in the District, Maryland and Northern Virginia. They serve nearly 1 million CareFirst members.

The program is based on a host of financial incentives. Doctors who join the program receive a 12 percent increase in their insurance reimbursements, plus $200 for each detailed care plan they set up for a patient. They can earn additional fees if their patients’ health-care costs at the end of last year were below expected costs.

Participating doctors work in groups of five to 15 clinicians. Last year, 253 such groups took part for at least six months and so were eligible for the additional fees.

Of those, nearly 60 percent of the teams cut their patients’ overall health-care costs by an average of 4.2 percent.

The program’s health-care costs totaled about $2.5 billion last year.

CareFirst will pay about $23 million in additional fees to those doctors from July 1 to June 30, 2013. They will receive an average 20 percent increase in fee payments from the insurer.