The bill, which has bipartisan support, was approved on a voice vote. Senate versions of the legislation are still pending in committee.
"Repealing the 3 percent withholding rule is a major step toward reducing uncertainty for businesses and allowing job creators to hire," said Rep. Dave Camp (R-Mich.), the committee chairman, in a statement.
Under the law -- which had already been delayed several times and wasn't set to take effect until 2013 -- all levels of government would be required to take 3 percent of each payment they make to vendors and other contractors and hand it over to the federal government. Upon paying federal taxes, those businesses could then reclaim the 3 percent.
The policy was designed to ensure that businesses working with all levels of government pay their federal taxes. But state and local leaders believe that, realistically, the policy would simply cause businesses to raise the prices they charge governments by 3 percent so they wouldn't have to wait around for their money.
State and local officials also argue that the law would create extra software and training costs as they integrated the rule into their existing payment systems. The policy was originally scheduled to take effect this year before having several delays.