Aetna aims to spend about $35 billion to buy rival Humana and become the latest health insurer bulking up on government business as the industry adjusts to the federal health care overhaul.

The proposed cash-and-stock deal, announced early Friday, would make Aetna a sizeable player in the rapidly growing Medicare Advantage business, which offers privately run versions of the federally funded health care program for the elderly and some people with disabilities.

The combination also would bolster Aetna’s presence in the state- and federally funded Medicaid program and Tricare coverage for military personnel and their families.

Health insurers are eager to do more business with government payers due in part to a Medicaid expansion fostered by the health care overhaul and Medicare Advantage’s surging enrollment. The overhaul is expanding Medicaid coverage in several states as it seeks to provide health coverage for millions of uninsured people.

Meanwhile, total enrollment in Medicare Advantage plans has tripled over the past decade to about 16.8 million people and is expected to keep growing as more baby boomers become eligible for the plans. Aetna’s acquisition of Humana would make it the largest provider of Medicare Advantage coverage, with 4.4 million members, a figure that could change depending on regulatory review.

“Government markets are the most rapidly growing aspect of the system,” said Dan Mendelson, CEO of the market research firm Avalere Health.

Hartford, Conn.-based Aetna announced its deal a day after the Medicaid coverage provider Centene Corp. said it would spend $6.3 billion to buy fellow insurer Health Net. That deal would help Centene expand in the nation’s biggest Medicaid market, California, and give it a Medicare presence in several western states.

In addition to these deals, the Blue Cross-Blue Shield carrier Anthem went public late last month with an offer of more than $47 billion for another insurer, Cigna.

Health insurers see more advantages to these big combinations than a chance to build their government portfolios.

Major acquisitions can offer an infusion of new business at time when growth has slowed in the biggest part of their business, employer-sponsored health coverage. Plus more employers are opting to pay their own insurance claims and hire insurers to administer the coverage. That’s a less lucrative line of work for managed care companies.