More than a dozen states have enacted near-total bans on abortions, several of which have been put on hold by the courts.
Mr Gordon, who is a Republican, also said he would allow a separate, wider bill that bans abortion except in limited circumstances to become law on Sunday without his signature. Both this ban and the ban on abortion pills could face challenges in the courts. It is not clear when a wider ban would come into force.
Abortion pills a new front in culture wars after Roe v Wade
Even more states have placed restrictions on abortion medication, such as requiring an in-person visit to a doctor before obtaining a pill.