The ObamaCare replacement would repeal penalties for those who do not buy health insurance.
The legislation would also replace income-based subsidies to help with the cost of premiums with age-based tax credits.
Democrats immediately criticized the plan, saying it would drive up the costs of health care.
The Affordable Care Act helped 20 million previously uninsured Americans get health insurance.
However, increases in insurance premiums have irked many Americans.
The new plan would reduce the role of the federal government in helping Americans afford healthcare.
The White House said in a statement: “Today marks an important step toward restoring health care choices and affordability back to the American people.”
President Donald Trump looked forward to working with Congress to repeal and replace the law, it said.
He has described ObamaCare, which was passed in 2010 and is seen as Barack Obama’s signature domestic policy achievement, as “a disaster”.
The Republican Party has majorities in both chambers of Congress but divisions remain on the details of what should replace ObamaCare, which is popular in many states, including some governed by Republicans.
The new legislation is expected to cover fewer people than those who gained insurance under Barack Obama.
A group of four Republican senators have already said that a draft of the legislation they reviewed did not adequately protect low-income people who received Medicaid coverage under ObamaCare.
The proposal unveiled on March 6 would preserve some popular elements of the existing law, including allowing young people to remain on their parents’ insurance plans until the age of 26.
Insurers would also remain banned from denying coverage to those with pre-existing conditions.
While penalties for those who don’t buy health insurance would be scrapped, those who let their coverage lapse could see their premiums raised by 30% by insurers.
House Speaker Paul Ryan said the bill would “drive down costs, encourage competition, and give every American access to quality, affordable health insurance”.
He said no one would have “the rug pulled out from under them”.
However, some conservatives have already voiced concerns that the bill does not go far enough.
“It still looks like ObamaCare-lite to me,” said Senator Rand Paul.
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