Joe Biden has only been in office for a few days and already emphasises the importance of so-called "reproductive health".
The law in force so far permitted abortion only when the pregnancy was a result of rape or when it put the mother's life at risk.
The New York legislation on abortion is among the most permissive in the world.
A three-judge panel of the 8th U.S Circuit Court of Appeals sided with a lower district court’s 2019 ruling blocking the measures.
The President of Brazil referred to the legalisation of abortion-on-demand in Argentina this week.
Until now, only Uruguay, Cuba, Guyana and parts of Mexico have allowed the partial legalisation of killing the unborn on request.
Charlie Baker, the pro-choice Republican governor of Massachusetts vetoed the bill.
The pro-abortion groups are determined to "push through" the regulations this year, given that elections will take place in 2021
For the Republican governor of Tennessee, Bill Lee, the sentence means victory in a battle - though not a war - to save life.