Senators debating a health care overhaul waded into the difficult issue of abortion on Wednesday, defeating an amendment that would have tightened federal restrictions on the procedure.

The Senate Finance Committee voted 10-13 against a bid by Orrin G. Hatch , R-Utah, to bar any insurer receiving federal funds from covering abortion, unless women used their own money to buy auxiliary policies covering the procedure.

Democrats called Hatch’s amendment discriminatory and said it would upset a delicate balance that Finance Chairman Max Baucus , D-Mont., had attempted to strike on the issue.

“With all due respect to my friend,” Debbie Stabenow , D-Mich., said to Hatch, “as a woman I find it offensive.”

Democrats have tried all year to tamp down a simmering controversy over whether their health care overhaul would increase the number of abortions performed in the country. Both the House and Senate bills include language that would require insurers to pay for abortions using only funds from premiums people pay for their policies, not tax dollars.

But abortion opponents, led by the National Right to Life Committee, say that by expanding federally-subsidized insurance coverage to millions of Americans without explicitly prohibiting the policies from covering abortions, there will inevitably be more pregnancy terminations.

Federal health programs, such as Medicaid and the military’s Tricare program, are currently prohibited from paying for abortions by riders attached to appropriations bills and renewed annually. Hatch’s amendment in essence sought to codify those riders and expand the scope to private insurance plans receiving tax dollars.

“If the intent of the committee is that we don’t want to fund abortion, let’s be very clear,” Hatch said.

Every Democrat on the committee except Kent Conrad of North Dakota voted against the amendment, while every Republican except Olympia J. Snowe of Maine voted for it.