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.
Republicans have overwhelmingly approved a resolution allowing states to withhold funds from abortion providers such as Planned Parenthood.