Aetna, one of the nation’s biggest health insurers, claimed a bigger stake in the burgeoning market for government-funded coverage Monday when it announced plans to buy a leading provider of Medicaid and Medicare coverage for $5.7 billion.

The Hartford, Conn., company’s proposed acquisition of insurer Coventry Health Care will bolster its Medicaid business a few months before millions of people are expected to become eligible for the state- and federally funded program for the needy and those with disabilities under President Obama’s health care overhaul.

It also will boost the company’s portion of business from the federally funded Medicare program, which covers seniors older than 65 and those with disabilities, at a time when interest in these plans is growing in part because the baby boomers are aging.

The deal underscores the major changes taking place in the health care industry as a result of the landmark overhaul.

The deal also marks the second time since the Supreme Court upheld the law in June that a big insurer has snapped up a smaller company focused on government coverage.

Last month, WellPoint Inc., which offers Blue Cross-Blue Shield plans in 14 states, announced a $4.46 billion deal to buy Amerigroup Corp., and more acquisitions are likely.

Aetna is the nation’s third-largest health insurer based on enrollment, trailing only UnitedHealth Group Inc. and WellPoint. Coventry, a smaller insurer, is one of the leading providers of both Medicaid and Medicare-based coverage.

States hire insurers like Coventry to offer Medicaid coverage to their residents. Coventry said last month that its Medicaid enrollment had doubled to about 932,000 people.

It also provides Medicare prescription drug coverage to about 1.5 million people.