If anything, The Libertarian Party “punts” on the issue of abortion.
http://www.lp.org/issues/platform_all.shtml#reprodright
I.8 Reproductive Rights
The Issue: The tragedies caused by unplanned, unwanted pregnancies are aggravated and sometimes created by government policies of censorship, restriction, regulation and prohibition.
Recognizing that abortion is a sensitive issue and that people can hold good-faith views on both sides, we believe that government should be kept out of the matter, leaving the question to each person for their conscientious consideration.
The Principle: Individual rights should not be denied nor abridged on the basis of sex, age, dependency, or location. Taxpayers should not be forced to pay for other people’s abortions, nor should any government or individual force a woman to have an abortion. It is the right and obligation of the pregnant woman regardless of age, not the state, to decide the desirability or appropriateness of prenatal testing, Caesarean births, fetal surgery, voluntary surrogacy arrangements and/or home births.
Solutions: We oppose government actions that either compel or prohibit abortion, sterilization or any other form of birth control. Specifically we condemn the practice of forced sterilization of welfare recipients, or of mentally retarded or “genetically defective” individual. We support the voluntary exchange of goods, services or information regarding human sexuality, reproduction, birth control or related medical or biological technologies. We oppose government laws and policies that restrict the opportunity to choose alternatives to abortion.