Approval on final action Wednesday would send the measure to the Senate. The Republican-dominated House has an anti-abortion majority, so the measure was expected to pass.
Senate GOP leaders are promising their chamber will consider the bill quickly.
The bill would prevent groups providing abortions from receiving tax exemptions or credits that go to other nonprofit groups or health care providers. It would also bar women who claim income tax deductions for medical expenses from including the cost of abortion services.
The legislation also prohibits abortion providers from furnishing materials or instructors for sex education classes in schools.