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A US federal judge has ordered the Trump administration to continue an Obama-era programme for undocumented migrants, dealing a huge blow to the president's plans to have it scrapped.

US District Judge John Bates on Tuesday described the government's phasing out of the Deferred Action for Childhood Arrivals program as "virtually unexplained" and therefore "unlawful."

Bates said that the government decision to begin ending the programme in March "was arbitrary and capricious because the Department failed adequately to explain its conclusion that the program was unlawful."

The judge's ruling will take effect in 90 days, allowing the Trump administration time to produce a stronger case for ending the programme.

Bates said if a more solid reason is not provided by the government, the Department for Homeland Security must accept and process new as well as renewal DACA applications."

Introduced in 2012, the DACA programme allowed immigrants brought to the US illegally as children, known as Dreamers, to stay and work legally under renewable permits.

US President Donald Trump declared earlier this month the Obama-era programme is a thing of the past in an attack on Democrats currently attempting to defend DACA.

"DACA is dead because the Democrats didn't care or act, and now everyone wants to get onto the DACA bandwagon," Trump tweeted.

It "[n]o longer works. Must build Wall and secure our borders with proper Border legislation. Democrats want No Borders, hence drugs and crime!," he continued.

Bates' decision on Tuesday made him the third US judge to rule against the government's plans to phase out DACA.