The United States Supreme Court kept its hands off and simply ignored an appeal from North Dakota that would have prevented the killing of innocent unborn children in the state.

On Tuesday, the justices of America's highest court refused to take up North Dakota's petition to revive its proposed restriction on abortions, which was earlier struck down by lower courts.

North Dakota passed a state law in 2013 that declared as illegal those abortions that were performed after heartbeat could be detected from a foetus, or the period about six weeks into a mother's pregnancy.

The U.S. Court of Appeals for the Eighth Circuit initially blocked North Dakota's abortion restriction, saying that earlier Supreme Court decisions already prevented states from imposing undue burden on American women's right to choose during the period of pregnancy before the foetus is viable.

The court essentially sided with the Center for Reproductive Rights, which represented the lone abortion clinic in North Dakota.

"Since this Court first recognised constitutional protection for pre-viability abortion, two generations of American women have come of age, depending on constitutional protection for their dignity in making reproductive decisions," the pro-abortion group argued.

The appeals court nevertheless said there exist "good reasons" for the Supreme Court to revisit previous cases that tackled abortion.

"The continued application of the Supreme Court's viability standard discounts the legislative branch's recognised interest in protecting unborn children," the Eighth Circuit said in the North Dakota case, as quoted by NBC News.

Earlier this month, the Supreme Court also refused to rule on an appeal filed by state officials from Arkansas seeking to revive a similar foetal heartbeat law, which banned abortions after about 12 weeks of pregnancy.

The high court is also set to decide on a Texas law requiring doctors performing abortions to have admitting privileges at nearby hospitals.