Five Texas women who were denied abortions despite serious complications have sued the conservative US state, asking a judge to clarify exceptions to the new laws.

It is the first such complaint filed by women who have been denied terminations since the US Supreme Court overturned abortion rights in June, according to the Center for Reproductive Rights, which represents them.

The lawsuit, filed late Monday, "includes devastating, first-hand accounts of women's lives almost lost after they were denied the health care they needed," said Vice President Kamala Harris, who gave them her support in a statement Tuesday.

White House Press Secretary Karine Jean-Pierre called the details "shameful and unacceptable."

"Horrifying details of needless pain," the spokeswoman for Democratic President Joe Biden said in a statement. "All because of extreme efforts by Republican officials to take away a woman's right to choose."

The women, who will speak at a press conference later Tuesday, wanted to carry their pregnancies to term but discovered during medical examinations that their fetuses were not viable.

In their complaint, they claim that their doctors refused to perform abortions despite the risks of hemorrhage and infection.

They blame those refusals on the various laws prohibiting abortions in Texas, one of which provides for up to 99 years in prison for doctors who defy the ban.

These laws allow for limited exceptions in case of medical emergencies, such as the threat of death or serious disability to the mother -- but the plaintiffs say they are too vague.

One of them, 35-year-old Amanda Zurawski, had her water break at 17 weeks, far too early for the fetus to survive.

However, her hospital waited for three days -- until she showed signs of infection -- before delivering the fetus.

According to the complaint, "she nearly lost her own life and spent days in the ICU for septic infections whose lasting impacts threaten her fertility and, at a minimum, make it more difficult, if not impossible, to get pregnant again."

Another, Lauren Miller, was pregnant with twins when she learned that one of the two fetuses was not viable.

Despite the risks to her own health and the development of the other fetus, medical staff would not perform an abortion on the nonviable fetus and she had to travel to Colorado, at her own expense, to get the procedure.

Still pregnant, she is due at the end of the month.

At 18 weeks of pregnancy, Lauren Hall discovered that her fetus had no skull and would not survive. She had to travel to Seattle to have the pregnancy terminated.

Unlike the other complaints filed by doctors or associations since June, this appeal does not attack the abortion ban but asks the courts to "clarify the scope of the exception."