Abortion and reproductive rights advocates filed a lawsuit on Tuesday against legislation that would impose the nation's toughest anti-abortion ban on women in North Dakota.

It is the latest of several anti-abortion measures in the state advocates say are unconstitutional and represent and "all-out assault on women's rights."

The lawsuit challenges two recently passed North Dakota laws, one of which bans abortions as early as six weeks of pregnancy, when a foetal heartbeat can be detected. It would ban abortion before most women even know they are pregnant, leaving them with no option by the time they find out.

The other, which seeks to ban the procedure when the foetus has a genetic abnormality, including one that could be lethal, or for sex selection reasons, is the first of its kind in the US.

It is the third suit filed by the Center for Reproductive Rights against a slew of North Dakota laws aimed at making the state abortion free. The CRR, acting on behalf of the state's only abortion clinic, the Red River Women's Clinic, in Fargo, and its medical director, argues that the laws are unconstitutional and could harm women.

The state, one of four across the US with only one abortion clinic, was rated among the worst in the US for access to women's reproductive services in a report this year by Naral Pro-Choice America.

The lawsuit seeks to stop both laws, which have been passed, from coming into effect on 1 August.

The two North Dakota measures are among four signed into law by the state's Republican governor Jack Dalrymple this year with overwhelming support by the state's Republican-led legislature.

Jeff Zent, a spokesman for Dalrymple, said it's the governor's "standing policy not to comment on litigation".

Janet Crepps, an attorney for the Center for Reproductive Rights, told the Guardian that the law would ban abortion even in the cases where a foetus has a genetic abnormality that could prove fatal.

"It is a radical shift away from the legal position where you can decide your reasons for an abortion. One you start saying this reason is okay and that reason is not, it is a slippery slope to saying 'none of them' are appropriate."

Nancy Northup, president and CEO of the Center for Reproductive Rights, said the measures would endanger women's lives and would interfere in private medical decisions between a woman and her doctor that are currently protected by the constitution and "more than 40 years of US supreme court precedent".

Northup said: "In their scorched-earth campaign to rid North Dakota of its only reproductive health clinic that provides abortions and effectively end safe, legal abortion in the state, the politicians who advanced these laws made their hostility to women clear.

"They would relegate the women of North Dakota to a second class of citizens whose rights and access to reproductive health care are not equal to those who live in states committed to defending the rights of their citizens rather than attacking them."

Tammi Kromenaker, director of the Red River Women's Clinic, which performs between 1,200 and 1,300 terminations a year, has warned that if the measures come into effect, it would drive women to back-street abortions. She said: "Such an extreme ban on abortion would have a devastating impact on women in North Dakota and our neighboring states, especially those who do not have the resources to travel hundreds of miles to access reproductive health care."

With a series of extreme anti-abortion laws, passed by the legislature, North Dakota has recently emerged as the latest front in the country's bitter battle over abortion and reproductive rights.

This month, the American Civil Liberties Union declared 2013 to be one of the "most regressive yet" when it comes to taking away access to safe, legal abortion.

The ACLU charted a "cumulative set of restrictions" this year, added to restrictions in previous years, which has meant fewer clinics, more obstacles to health care, and "women being told we are too stupid to make decisions for ourselves" Louise Melling, ACLU's legal director, said in a press release.

They include a 20-week abortion ban in Arkansas, a Kansas law that requires doctors to provide information about a link between breast cancer and abortion which has been rejected by medical experts. Eleven states including North Dakota ban medication abortion and seven states, including North Dakota and Mississippi, have laws that would unnecessarily require doctors in abortion clinics to have admitting privileges. These laws are also being challenged by the CRR.

In the early hours of Wednesday, a measure to limit abortion in Texas was defeated after a marathon filibuster and a public protest.

The Roe vs Wade supreme court ruling established that a woman has the right to an abortion until the foetus is viable outside the womb, around the 24th week of pregnancy.

Attempts to limit abortions to below 20 weeks in Arizona, Georgia and Idaho have been blocked by court rulings. Other measures to require admitting privileges to doctors in abortion clinics are being challenged in Alabama and Mississippi.