The ruling comes as legal challenges over the laws persist, and the court hasted the timeline for lawsuits to be decided.
Two justices approved of hastening the cases but stressed that they felt laws should not be enforced until the legal process has been completed.
A doctor and a regional Planned Parenthood sued Idaho over three anti-abortion laws.
The Justice Department is also suing Idaho in federal court over a near-total abortion ban; the judge has not yet led in that case.
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The state Supreme Court's ruling means that potential relatives of an embryo or fetus can now sue abortion providers over procedures done after six weeks of gestation. Another stricter ban criminalizing all abortions is expected for later in August.
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Potential relatives can sue for up to $20,000 within four years of abortion. While rapists cannot sue under the law, a rapist’s family members would be able to sue.
On Aug. 25, per the Idaho Supreme Court's decision, a near-total criminalizing of all abortions – still allowing doctors to protect themselves at trial by claiming the abortion was done to save the pregnant person’s life – will happen.
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Planned Parenthood has also sued over a third ban that criminalizes abortions done after six weeks of gestation except in cases where it was needed to save a pregnant person’s life or done because of rape or incest.
That law was written to take effect on Aug. 19.
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The Supreme Court said the plaintiffs did not demonstrate that allowing enforcement of the laws would cause "irreparable harm" and that there was not enough evidence that they had a "clear right" to a remedy.
"What Petitioners are asking this court to ultimately do is to declare a right to abortion under the Idaho Constitution when – on its face – there is none," Justice Robin Brody wrote for the majority.
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"The State and the Legislature’s only argument that irreparable harm will not result is that the Idaho Constitution does not protect the right to an abortion," Justice John Stegner wrote in a partial dissent.
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"This argument fails because it is premised on a decision we have not yet made."
This ruling comes as other states face similar challenges following the U.S. Supreme Court's decision to overturn Roe v. Wade.
In nearby Wyoming, a judge blocked the state's near-total ban on Wednesday.
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The Louisiana Supreme Court on Friday denied an appeal filed by plaintiffs, allowing the ban there to stay in effect.
In Kansas, the elections director said the state would go along with a request for a hand recount of votes from every county after last week's decisive statewide vote affirming abortion rights.
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