US President Joe Biden has condemned a new law in Texas banning abortion from as early as six weeks and vowed to defend women's constitutional rights.

The "extreme" law "blatantly" violated rights and would "significantly impair" women's access to healthcare, he said.

On Wednesday the Supreme Court refused, by a 5-4 vote, to block the new law.

The law bans abortions after detection of what anti-abortion campaigners call a foetal heartbeat - a point when many women do not know they are pregnant.

The so-called Heartbeat Act also gives any individual the right to sue doctors who perform an abortion past the six-week point.

Doctors and women's rights groups have heavily criticised the law, which is one of the most restrictive in the country, and took effect after the conservative-leaning Supreme Court failed to respond to an emergency appeal.

Abortion and women's health providers had filed an emergency request to the Supreme Court calling for an injunction on enforcement of the ban.

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

In a dissenting opinion, liberal Justice Sonia Sotomayor wrote that the court's order was "stunning".

"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," she said.

In his statement, President Biden said his administration would "protect and defend" the constitutional rights established under Roe v Wade and "upheld as a precedent for nearly half a century".

He was referring to the 1973 case in which the Supreme Court ruled US women have the right to an abortion until a foetus is viable - that is, able to survive outside the womb. This is usually between 22 and 24 weeks into a pregnancy.

White House spokeswoman Jen Psaki told reporters that the president had long wanted to see the "codification" of Roe v Wade - which would mean Congress voting to make the precedent federal law - "and [the Texas law] highlights even further the need to move forward on that effort".

Other Democrats also expressed their outrage. House Speaker Nancy Pelosi said the Supreme Court had "delivered catastrophe to women in Texas" while New York Mayor Bill de Blasio said it was a "direct assault on the rights of women" across the country and would need a "national mobilisation" to fight it.

Rights groups, including Planned Parenthood and the American Civil Liberties Union (ACLU) who had requested that the Supreme Court block the legislation, say they will not give up the fight.