The proportion of Americans without health insurance has fallen by more than a third since the start of the Affordable Care Act, according to new government estimates that are likely to strengthen efforts to prevent Barack Obama’s flagship domestic reforms being rolled back by political opponents.

A total of 14.1 million adults are thought to have gained insurance since the act – known as Obamacare – went into full effect in October 2013, with a further 2.3 million younger adults benefitting from new rules that allow those aged 19-25 to remain on their parents’ insurance plans.

Together these net gains have reduced the national uninsured rate from 20.3% to 13.2%, or a total of 16.4 million people, based on government analysis of recent survey data.

Though tentative, the statistics may help the White House argue that its reforms are too well entrenched for future administrations to unpick – something many leading Republicans in Congress have called for due to their fierce opposition to the compulsory elements of the scheme.

The supreme court is also currently considering a legal challenge sponsored by Obamacare’s opponents that could reverse a vital subsidy included in the reforms after a dispute over the wording of the original legislation.

Though critics remain sceptical about many aspects of the reforms, both the supreme court justices and Republican candidates for president in 2016 will now have to consider the political consequences of unravelling a package that has brought health insurance to a nationwide group almost as large as the total population of New England.

But the figures also show how many more Americans are still without insurance despite the reforms, which compel adults to buy insurance or employers to offer it only in certain circumstances. Some 26.3 million adults remain without insurance of their own.

Officials say they expect the growth trend among those insured to continue, though they acknowledge they know little about the millions of Americans who are still without coverage.

“We are entering new territory here,” Richard Frank, the assistant secretary for planning and evaluation at the Department of Health and Human Services, told reporters on a conference call.

“We are just starting to understand more completely who we have really brought in and also who is left uncovered.”

The department’s analysis also shows a clear difference between states that have allowed an extension of Medicaid, a program which covers many poorer families, and those that have resisted it.

The 29 mostly Democratic-controlled Medicaid expansion states saw their uninsured rates fall by 7.4% over the period, while those who have refused to accept the federal funding to expand the scheme saw a 6.9% fall.

Nevertheless, the largest source of the rise in insurance cover has been new individuals signing up through so-called healthcare exchanges, which are available in all states, either through locally run systems or via the federal exchange.

This federal exchange in particular had an extremely rocky start due to computer glitches and delays to associated tax reforms, but figures released last week showed 11.7 million people had now signed up or renewed their insurance by 22 February.