President Donald Trump has said he will "immediately" ask the US Supreme Court to rehear a case challenging birthright citizenship.

It comes a week after the high court ruled that those born in the US have a constitutional right to citizenship, rejecting Trump's executive order that sought to restrict the 150-year-old policy.

While the Supreme Court allows for such a request, the high court has rarely ever granted a rehearing. The last time a decided case was reheard was some 60 years ago.

"This miscarriage of justice will destroy America if they don't change their absolutely insane decision," Trump wrote on social media on Wednesday.

The high court's rules allow for a losing party to formally file a request for a rehearing within 25 days. A majority of the nine-member court would have to approve granting a rehearing.

The 30 June ruling to uphold birthright citizenship marked a setback for the president's immigration agenda, though it was welcomed by civil rights groups.

In a 6-3 decision, Chief Justice John Roberts ruled that children born in the US "to parents unlawfully or temporarily present" are "citizens at birth" under the 14th Amendment of the US Constitution.

Trump had sought to limit the right through an executive order, arguing that the children of undocumented immigrants and some temporary visitors were not "subject to the jurisdiction thereof", and thus not eligible for birthright citizenship.

Five of the justices, including Chief Justice Roberts, agreed that Trump's executive order violates the Constitution's 14th Amendment. Justice Brett Kavanaugh wrote separately to say he believed Trump's order violated federal law.

After the ruling was issued, Trump vowed to continue to fight to end birthright citizenship through legislation, which would need passage through the US Congress.

The US has granted citizenship to everyone born in the country since 1868, with the right enshrined in the 14th Amendment of the US Constitution, and bolstered by later US Supreme Court rulings.