The House of Representatives passed HJ Res 43 on Thursday by a mainly party line vote of 230 to 188.
The repeal proposal is expected to pass the Senate and be signed into law by President Donald Trump.
A number of measures to curtail access to abortion have been introduced by US state legislatures already this year.
Republicans have vowed to "defund" Planned Parenthood, a women's reproductive health organisation that provides birth control, STD testing, cancer screenings, breast examinations and pregnancy terminations.
HJ Res 43 would overturn a rule instituted two days before Mr Trump came into office.
The Obama administration measure banned states from withholding federal dollars from groups that provide abortions.
The rule was instituted after more than a dozen conservative states denied funds to Planned Parenthood through a Nixon-era family-planning programme known as Title X.
Planned Parenthood receives hundreds of millions of dollars a year in funding from the federal government, but it is banned by law from using any of that money to fund abortions.
Anti-abortion Republicans cheered the first step to overturning the Obama administration rule.
New Jersey Representative Chris Smith said: "Planned Parenthood is Child Abuse Inc," referring to secretly recorded footage of employees at the group discussing foetal tissue donation.
But critics warned that low-income and young women would bear the brunt of HJ Res 43.
Democratic Congresswomen Diana DeGette said: "Despite their promise to focus on jobs and the economy, Republican leaders have made attacking women's health care their top priority."
Planned Parenthood President Cecile Richards condemned Republican "extremists" who had backed HJ Res 43.
This week, an Oklahoma bill which would force women to get permission from their sexual partner for an abortion passed its first hurdle.

Police and the British Army's Explosive Ordnance Disposal (EOD) team were called to Motorhog in Empire Way at 12:15 BST on Friday.
Part of Bristol Road was closed and nearby properties were evacuated while a controlled explosion was carried out.
Police have confirmed there were no explosives in the package and are now investigating.

The Medway Queen took more than 7,000 trapped men from beaches in 1940.
Restoration work began last year with help from the Heritage Lottery Fund and the European Regional Development Fund.
The government said administrative errors had led to the suspension of EU funding and it was working to get payments released.
Restoration work on the ship's hull began in Bristol last April with money from a ??1.86m Heritage Lottery Grant.
Medway Council applied to the European Regional Development Fund for a grant to complete the restoration and bring the ship home.
The final stages of the project are being undertaken at a workshop in Gillingham by 16 people, including nine young apprentices whose jobs are now under threat, as there is only enough money until the end of April.
Peter Skinner, Labour MEP for the South East, said EU funding to all UK partners within the Interreg 2 Seas programme had been suspended after the UK government failed to meet the standards demanded by auditors.
He said the problems had nothing to do with the Medway Queen project.
"The Medway Queen has taken on local young people and is giving them practical work skills through apprenticeships.
"Through no fault of theirs funding has been suspended. That can't be right," Mr Skinner said.
"I've been pushing ministers; they need to find a solution. I have also demanded a meeting with the [European] commissioner. I want him on the case.
"The project is a great opportunity for the apprentices and they shouldn't be in danger of losing out because of some bureaucratic foul up."
In a statement, the Department for Communities and Local Government said: "This funding programme is run by a managing authority in Nord-Pas de Calais, France.
"Nevertheless, the department is very disappointed with the European Commission's decision to withhold payments to UK project partners and we are working intensively to get these payments released."
Republicans have overwhelmingly approved a resolution allowing states to withhold funds from abortion providers such as Planned Parenthood.
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A suspicious package discovered at a vehicle dismantler's yard in Gloucester was "not a bomb", police have said.
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The restoration of a paddle steamer which rescued Allied troops during the Dunkirk evacuations is under threat after European funding was suspended.