WASHINGTON (Reuters) - The U.S. House of Representatives added another notch to its lengthy record of Obamacare repeal votes on Tuesday by approving a measure that would scrap the healthcare law and direct oversight committees to come up with a replacement.

Defying a White House veto threat, lawmakers voted 239-186 on a measure to eliminate the complex web of federal subsidies, insurance reforms, taxes and regulations that have extended health coverage to millions of Americans since the Affordable Care Act became law in 2010.

The action now moves to the Senate, where Republican Senator Ted Cruz, a Texas conservative, introduced legislation for full repeal on Monday.

The influential conservative group Heritage Action for America called the House vote "the beginning of a multi-month effort" to send a full repeal legislation to President Barack Obama's desk.

The White House threatened to veto the House bill, saying it would take away critical benefits from middle-class families and increase the federal deficit.

Before the vote, Obama met with 10 people who had benefited from his signature domestic policy. He told reporters the law was working "better than intended."

Supporters of repeal are short of the two-thirds majority needed in both chambers of Congress to override a presidential veto.

The House has voted repeatedly to repeal, defund or dismantle Obamacare.

But on Tuesday, Republicans and Democrats could not agree on how many times. Republican aides said the new vote brought the total to 67, including eight votes for full repeal. Democrats said there had been 56 votes to repeal or undermine the law.

The House's second anti-Obamacare vote of 2015 was billed by Republican lawmakers as a way to give party freshmen a crack at repealing the law. Last month, lawmakers voted to scale back an Obamacare provision requiring employers to provide workers with health insurance.

Tuesday's bill also directed House committees to work toward Republican legislation to replace Obamacare, a goal that has eluded the party repeatedly up to now.

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Lawmakers said new legislation would be necessary in light of a U.S. Supreme Court case that could devastate Obamacare by denying federal insurance subsidies to millions of consumers in as many as 37 states served by the federal website, HealthCare.gov. A ruling is expected in June.

Obamacare advocates said Republicans were trying to persuade the Supreme Court to vote against the law by promoting a legislative goal they could not actually achieve.

(Reporting by David Morgan, Roberta Rampton and Susan Cornwell; Editing by Emily Stephenson, Sandra Maler and Peter Cooney)