North Dakota’s Republican governor Jack Dalrymple has signed legislation outlawing abortions after 20 weeks of pregnancy based on the disputed premise that at that point a foetus can feel pain.

The law is the latest among a raft of measures passed in North Dakota this session that are meant to challenge the US supreme court’s 1973 Roe v Wade ruling that legalised abortion up until viability, usually at 22 to 24 weeks.

Abortion-rights campaigners have called the laws unconstitutional and have promised a long legal fight that they say the state cannot win.

Dalrymple last month signed a law that bans abortion as early as six weeks, or when a foetal heartbeat is detected, making North Dakota the most restrictive state in the US to get the procedure.

Dalrymple also signed into law last month other measures that make the state the first to ban abortions based on genetic defects such as Down’s syndrome and require a doctor who performs abortions to be a physician with hospital-admitting privileges. The measures also ban abortion based on genetic selection.

Abortion-rights activists say the measures, which come into effect on 1 August, are aimed at closing the state’s sole abortion clinic, the Red River Women’s Clinic in Fargo.

At least 10 states have passed bills banning abortions after 20 weeks of pregnancy on the premise that a foetus can feel pain at that stage, but research is split on the theory.

North Dakota politicians also moved last month to seek a referendum defining life as starting at conception, in effect banning abortion in the state. The measure is likely to come before voters in November 2014.

The Centre for Reproductive Rights has said it is committed to challenging the foetal heartbeat bill on behalf of the Fargo clinic.

The New York-based group is representing the clinic for free in a trial that started on Tuesday over a 2011 law banning the widely accepted use of a medication that induces abortion. A judge has temporarily blocked enforcement of that law.

The Centre for Reproductive Rights also was part of a lawsuit filed on Tuesday that seeks to overturn the more restrictive of Arkansas’s two new abortion laws, saying the near-ban of abortions from the 12th week of pregnancy onward is unconstitutional.

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