(CNN) Democratic presidential candidate Pete Buttigieg unveiled his health care plan on Thursday, outlining a middle-of-the-road approach that allows people to opt into a government-backed health insurance option but lets them keep their private insurance plans if they like them.

The South Bend, Indiana, mayor calls his plan "Medicare for All Who Want It," a nod to the popularity of "Medicare for All," the Democratic health care proposal championed by Sen. Bernie Sanders of Vermont and backed by several other 2020 Democrats, which would represent a wholesale change to the American health care system.

Buttigieg's proposal -- unlike Sanders' plan -- would not force people onto government health coverage but instead would offer a public option for people who choose to enroll. Buttigieg has argued this would force private insurers to compete with the government-backed plan on price.

At the same time, he would enhance federal Affordable Care Act subsidies so more people could afford to buy policies on the exchanges.

The proposal, which bears many similarities to former Vice President Joe Biden's approach, further injects Buttigieg into the most contentious debate raging inside the Democratic Party, and one that polls show will directly impact who voters back in the 2020 primary. Buttigieg has tried to acknowledge the excitement around Medicare for All proposals by saying a single-payer system is a good long-term goal, but the mayor has also started to use the fact that Medicare for All would kick people off their private plans to subtly attack Sanders and others.

Buttigieg used the third Democratic debate earlier this month to question Sanders directly about his plan, turning to the senator and asking, "I trust the American people to make the right choice for them. Why don't you?"

And Buttigieg has taken this attack line directly to voters with ads on Facebook and other digital platforms. The mayor has begun sponsoring a post on Facebook that says, "Medicare for All Who Want It will create a public alternative, but unlike the Sanders-Elizabeth Warren vision it doesn't dictate it to the American people and risk further polarizing them." Another ad simply states, "I trust the American people to make their health care decisions for themselves."

Buttigieg said in a statement around his plan's release that American health care is "at this moment of crisis because of a failure of leadership."

"For years, Washington politicians have allowed the pharmaceutical industry, giant insurance companies, and powerful hospital systems to profit off of people when they are at their sickest and most vulnerable," he said. "My 'Medicare for All Who Want It' plan will create a health care system that puts power in the hands of each American."

The government-backed plan would be open to all, but those with lower incomes who live in states that have not expanded Medicaid would be automatically enrolled. Those who find their employer coverage too expensive could sign up for the public option and receive federal premium subsidies to help them afford it. And it would retroactively enroll the uninsured in the public option and reimburse providers for unpaid care through a backstop fund.

Buttigieg would boost federal subsidies by capping premiums at 8.5% of income for everyone purchasing coverage on the Obamacare exchanges. Currently, only those who earn less than 400% of the federal poverty level -- or about $100,000 annually for a family of four -- qualify for help lowering their premiums to just under 10% of their income.

Plus, the mayor would base those subsidies on the cost of "gold plans," which have higher premiums but lower deductibles, rather than less generous "silver plans." That means people could spend less out of pocket -- or could use the larger subsidies to buy less expensive silver or bronze plans.

The plan also outlines how, under a Buttigieg administration, the out-of-pocket costs of people on Medicare would be capped, with low-income seniors qualifying for the lowest caps. Currently, those enrolled in traditional Medicare have no limit on annual spending, unlike those in individual market or employer-based plans.

The mayor's proposal contains many of the same elements as Biden's plan, which was released in July. The former vice president would also create a public option, enhance Obamacare's subsidies and automatically enroll low-income Americans who live in states that did not expand Medicaid. Biden has hailed his plan as enhancing former President Barack Obama's Affordable Care Act. However, Biden has come under attack because his proposal says it would cover more than an estimated 97% of Americans, which would still leave 10 million people uninsured.

Both plans, as well as many of those issued by other candidates, have the same goal: expanding coverage and access to care, said Andy Slavitt, a former Obama administration official who was briefed on Buttigieg's proposal.

"It's a starting point in getting something passed that meets with the core principles that he has," said Slavitt, who has also praised other candidates' plans, including that of Sen. Kamala Harris of California, who unveiled her vision in July, which would transition the country to Medicare for All but retain a role for private insurers.

Buttigieg's plan would also look to end "surprise" medical billing, a practice that often occurs when a patient receives care from a hospital that is within their insurance network but is treated by a doctor who is out of network. Congress is trying to tackle this issue, but its bipartisan efforts are being hamstrung by heavy lobbying from doctors, hospitals and insurers.

To end surprise billing, Buttigieg's plan would require that all providers at in-network hospitals be billed as in network even if the doctors or labs are out of network.

"Hospitals, not patients, should bear the responsibility of verifying that their providers are included in their insurance networks, whether for private plans or public programs," reads Buttigieg's plan.

Health care is in the spotlight in the Democratic primary contest and represented the central issue that the party rode to a majority in the House of Representative during the 2018 midterm elections.

And the debate over Medicare for All has been one of the most contentious of the primary, with Medicare for All being the plan most popular with the liberal wing of the Democratic Party. Some of the party's more moderate voices have used Medicare for All as a way to attack the party's left, including Sanders, by pointing out that it would kick millions of Americans off private health insurance plans that, by and large, they enjoy.

Other questions have centered on how pro-Medicare for All candidates would pay for such a massive health care overhaul.

While Sanders has admitted that passing a Medicare for All bill would mean higher taxes for middle-class families, the senator argues that cost would be offset by lower out-of-pocket medical expenses. Two think tanks -- one on the right, one on the left -- have pegged the price tag of an earlier version of Medicare for All at $32 trillion over a decade.

Other candidates have not been as direct. Warren, a senator from Massachusetts, has waffled on how she would pay for the plan and Harris has ruled out a middle-class tax hike to pay for her plan, which led Biden's campaign to accuse her of not being "straight" with voters.

A Buttigieg aide said the mayor's plan would cost roughly $1.5 trillion over a decade and be "paid for by cost savings and corporate tax reform to ensure big corporations pay their fair share." Biden has said his proposal would cost roughly $740 billion over a decade.

Buttigieg's attacks on Medicare for All have centered on choice, not cost.

"If we're right, as progressives, that that public alternative is better," Buttigieg said at the September debate, "then the American people will figure that out for themselves."

He added: "I trust you to choose what makes the most sense for you. Not my way or the highway."

The rollout of Buttigieg's plan comes ahead of a four-day bus tour across Iowa that the candidate will embark on Saturday.