US President Joe Biden said he is launching a "whole-of-government effort," including from the White House counsel, to combat a strict new Texas abortion law after an overnight Supreme Court decision let it stand.

Mr Biden, a Democrat and a Catholic, has shifted to the left on abortion in recent years to be more in line with his party's base.

He has called the new Texas law that bans any abortion after six weeks an "unprecedented assault on a woman's constitutional rights".

The president said in a statement he was directing the office of the White House counsel and his Gender Policy Council to review how the US government could "ensure that women in Texas have access to safe and legal abortions".

He will examine "what legal tools we have to insulate women and providers from the impact of Texas' bizarre scheme of outsourced enforcement to private parties."

The US Supreme Court had earlier refused to block the Texan decree, dealing a major blow to abortion rights by leaving in place a state law that prohibits the vast majority of abortions.

The decision is a major milestone in the fight over abortion, as opponents have sought for decades to roll back access to the procedure.

By a 5-4 vote, the justices denied an emergency request by abortion and women's health providers for an injunction on enforcement of the ban, which took effect early yesterday, while litigation continues.

Sonia Sotomayor wrote a dissenting opinion

One of the court's six conservatives, Chief Justice John Roberts, joined its three liberals in dissent.

"The court's order is stunning," liberal Justice Sonia Sotomayor wrote in a dissenting opinion.

"Presented with an application to enjoin a flagrantly unconstitutional law engineered to prohibit women from exercising their constitutional rights and evade judicial scrutiny, a majority of justices have opted to bury their heads in the sand."

In an unsigned explanation, the court's majority said the decision was "not based on any conclusion about the constitutionality of Texas's law" and allowed legal challenges to proceed.

The law, known as the "Texas Heartbeat Act," bans abortion once a foetal heartbeat can be detected, which usually takes place at six weeks - before many women even know they are pregnant.

It makes no exceptions for rape or incest. The only exemption is if there is a danger to the woman's health.

While similar laws have passed in a dozen Republican-led conservative states, all had been stymied in the courts.

The American Civil Liberties Union (ACLU), Planned Parenthood, the Center for Reproductive Rights and other groups filed an emergency request with the Supreme Court on Monday asking it to stop the Texas law from taking effect.

But the court last night formally refused to block the legislation.

President Joe Biden vowed to defend abortion rights after the law took effect.

"This extreme Texas law blatantly violates the constitutional right established under Roe v. Wade and upheld as precedent for nearly half a century," Mr Biden said in a reference to the landmark 1973 Supreme Court case that legally enshrined a woman's right to an abortion.

Vanessa Rodriguez, senior manager for the contact centre of Planned Parenthood of Greater Texas, said patients were "scared, confused, angry."

"Texas politicians are taking away their right to make the decision" about terminating a pregnancy, Ms Rodriguez said.

Amy Hagstrom Miller, chief executive of Whole Woman's Health, said a clinic in Fort Worth, Texas, had performed abortions until 11.56pm local time on Tuesday.

"Our waiting room was filled with patients," she said.

"I woke up feeling deep sadness. I'm numb."

The ACLU said the impact of the bill will be "immediate and devastating."

"Access to almost all abortion has just been cut off for millions of people," the powerful civil rights association said.

According to the ACLU, "approximately 85 to 90%" of the women who obtain an abortion in Texas are at least six weeks into pregnancy.

Anti-abortion activists, however, were jubilant: "This is an historic moment in the fight to protect women and children from abortion," said Marjorie Dannenfelser, president of the anti-abortion nonprofit Susan B Anthony List.

The other states that have sought to enact restrictions on abortion in the early stages of pregnancy have been barred from doing so by rulings that cited protections granted in Roe v. Wade.

That decision guaranteed the right to an abortion in the US so long as the foetus is not viable outside the womb, which is usually the case until the 22nd to 24th week of pregnancy.

Texas' law is different from those of other states because it allows the public - rather than state officials such as prosecutors or health departments - to bring private civil suits to enforce the ban.

Citizens are encouraged to report doctors who perform abortions or anyone who helped facilitate the procedure.

The Texas law "creates a bounty hunting scheme that encourages the general public to bring costly and harassing lawsuits against anyone who they believe has violated the ban," the ACLU said.

"Anyone who successfully sues a health centre worker, an abortion provider, or any person who helps someone access an abortion after six weeks will be rewarded with at least $10,000, to be paid by the person sued," it said.

Nancy Northup, president of the Center for Reproductive Rights, said the Texas bill would force women to "travel out of state - in the middle of a pandemic - to receive constitutionally guaranteed health care."

"It's cruel, unconscionable, and unlawful."

For procedural reasons, this system makes it more difficult for federal courts to intervene, and they have so far refused to hear appeals against the Texas law.

The Supreme Court is also due to hear a case in the coming months involving a Mississippi law that prohibits abortions after the 15th week of pregnancy, except in cases of medical emergency or a severe foetal abnormality.

It will be the first abortion case considered by the nation's high court since former president Donald Trump cemented a conservative-leaning 6-3 majority on the nine-member panel.