Five-year-old Liam Conejo Ramos and his father have returned to their home in a Minneapolis suburb after being detained by US immigration officers and held at a detention facility in Texas, a lawmaker said on Sunday.

A federal judge on Saturday ordered the release of Adrian Conejo Arias and his son, whom immigration officers detained during a Minnesota raid. US Representative Joaquin Castro, a Texas Democrat, wrote in a social media post that he picked them up on Saturday night at the detention facility and escorted them back to Minnesota on Sunday.

"Liam is now home. With his hat and his backpack," Castro said. "We won't stop until all children and families are home."

A photo that went viral last month shows Liam wearing a blue bunny hat outside his house with federal agents standing nearby. He was one of four students detained by immigration officials in a Minneapolis suburb, according to the Columbia Heights Public School District.

The Ecuadorean boy and his father, who entered the United States legally as asylum applicants, had been held in a detention facility in Dilley, Texas.

US District Judge Fred Biery wrote in a ruling on Saturday the case had its genesis in "the ill-conceived and incompetently-implemented government pursuit of daily deportation quotas, apparently even if it requires traumatizing children."

Biery, appointed by former President Bill Clinton, cited the Constitution's requirement that an arrest warrant must be based on a judge finding probable cause of a crime. The use of "administrative warrants" issued by immigration officials "is called the fox guarding the henhouse," he wrote.

Democrats have called for reforms after large-scale enforcement operations in Minnesota and other states, and following two deadly shootings of US citizens in Minneapolis involving ICE agents. Those demands by Democratic lawmakers include mandatory body cameras, the end to roving patrols and halting the use of face masks.

Funding for the Homeland Security Department has been held up as Republicans and Democrats continue negotiating over a DHS bill. "We'll be talking about that in the near future," President Donald Trump told reporters on Sunday at his Mar-a-Lago club in Palm Beach, Florida.

Some Republican mayors also see a need for reforms. "We're generally encouraged that the administration seems to be exploring that pivot," Oklahoma City Mayor David Holt told CBS's "Face the Nation" on Sunday.

Mayors are "caught in a little bit of an impossible situation" with federal immigration enforcers' presence in cities, Holt said, adding events in Minneapolis threaten to erode the trust authorities have built over time with residents in cities.

Holt spoke the day after Trump ordered DHS to refrain from dealing with protesters unless federal property is threatened or local officials request help.