The move comes as abortion is expected to be an important issue during the US midterm elections.
Graham’s proposed legislation includes exceptions for rape, incest or to save the mother’s life.
The new legislation has little chance of making it to the Senate floor while Democrats hold the majority.
It would alsolikely face a veto by President Joe Biden.
Graham previously introduced similar legislation in the Senate that proposed a nationwide ban on abortions after 20 weeks.
