A bill to ban abortion after about six weeks from conception has been vetoed in Ohio by Governor John Kasich.

The so-called "heartbeat" bill would have outlawed terminations after the first heartbeat in the foetus was detected, usually about six weeks into a pregnancy and before many women realise they are pregnant.

But Kasich did sign a 20-week abortion bill, which puts the restriction at a similar point to 15 other US states. He said this option was the "best, most legally sound and sustainable approach to protecting the sanctity of human life".

The two bills arrived on Kasich's desk at the same time after the "heartbeat" bill was approved by the Republican-controlled state congress on Tuesday and the 20-week bill on Thursday last week.

Had Kasich not used his veto, the six-week ban would have passed. He said it would be unconstitutional and would face un-winnable legal battles.

"The State of Ohio will be forced to pay hundreds of thousands of taxpayer dollars to cover the legal fees for the pro-choice activists' lawyers," said Kasich.

Ohio lawmakers could still override the veto if they can muster three-fifths of both the state House and Senate to support the "heartbeat" ban.

The president and CEO of Planned Parenthood Advocates of Ohio objected to the measures.

"For the second time in a week, the Ohio Legislature has inserted itself into women's private and personal health care decisions," said Iris Harvey. "These bans are a deliberate attempt to make abortion illegal in the state of Ohio."

Critics of the 20-week ban see it as opening a way for a landmark 1973 Supreme Court ruling known as Roe V Wade to be overturned. That decision stated that abortion was legal until the foetus was viable, which is usually between 22 and 24 weeks.

But Marjorie Dannenfelser, president of the Washington-based pro-life Susan B Anthony List said the "bold" action in Ohio was a "rejection of the status quo".

She said last week: "Americans reject the status quo of abortion on-demand, especially painful late-term abortions.

"Instead, voters and lawmakers are recognising the humanity of the unborn child: its heartbeat around six weeks and the pain the child can feel at 20 weeks."

President-elect Trump called for a total ban on abortion during his presidential campaign but has since softened this stance, saying he supports it in exceptional cases such as rape or where the mother's life is in danger. He has also called for an end to federal funding of Planned Parenthood, a pregnancy clinic that supports abortions.