The Justice Department has asked a federal judge in Chicago not to immediately reunite two Brazilian boys, being held in the city, with their fathers who are being held in New Mexico after allegedly trying to illegally enter the United States.

Meanwhile, another Brazilian mother detained at the border — but out of custody since June 13 — is asking a judge through a new lawsuit filed Monday to reunite her with her 10-year-old son, who was held here after her arrest for illegal entry.

The woman claims her son was sick when he was taken from her May 24, and she had no idea “where he had been taken, who was caring for him, or whether his health had improved or worsened.” Nearly three weeks ago, she tracked him down in Chicago, and she was allowed a brief visit with him Thursday.

A judge in California already ordered the government last month to reunite all separated families with children five or over within 30 days. Justice Department lawyers pointed to that order in a brief filed Monday as they argued two of the boys held in Chicago, 9 and 15, should not be immediately reunited with their fathers.

“Implementation of the requirements of that order are underway, and the government is devoting significant resources to facilitating compliance for all class members,” the government lawyers wrote. “The government, and the public, have an interest allowing these efforts to move forward without the issuance of other orders from other district courts that may impact these compliance efforts.”

The 9-year-old and 15-year-old are known publicly only as C.D.A. and W.S.R., respectively. So far, U.S. District Judge Edmond Chang has ordered the government only to not deport the boys’ fathers without them. Lawyers are expected back in Chang’s courtroom Thursday.

The Brazilian children are among an untold number wo have been held in Chicago under the Trump administration’s “zero tolerance” immigration policy. They are in shelters run by Heartland Alliance, which has a contract with the Office of Refugee Resettlement.

The Chicago Sun-Times gave a glimpse into the children’s lives here — and published drawings by C.D.A. — in a front-page story Sunday. Heartland has since been dismissed from the lawsuits filed by attorneys representing C.D.A. and W.S.R.

In its brief asking Chang to reject the request by C.D.A. and W.S.R., the Justice Department described the boys’ fathers as “aliens who were seeking to enter the United States without any documentation allowing for their admission.” The fathers were “prosecuted for illegal entry” and placed into the custody of the U.S. Marshals.

Lawyers for the boys say both fathers first tried to enter the United States through a Port of Entry, only to be turned away. The lawyers also want the fathers released.

The Justice Department said the fathers’ arrest meant the boys had “no parent or legal guardian in the United States.” Its lawyers also wrote that the boys “ask this court to recognize a constitutional right for children not to be held in government custody separately from their parents, despite the fact that their parents are lawfully in immigration detention.”

They insisted that, to show a due process violation, the boys “must establish that the government has engaged in conduct that is so outrageous that it shocks the conscience.”

Last week, U.S. District Judge Manish Shah ordered the immediate release of a 9-year-old Brazilian boy held in Chicago, Diogo, to his mother, Lidia Souza. Though Souza had also been accused of trying to enter the country illegally, she had been released on her own recognizance.

Souza shares lawyers with the woman now trying to reunite with her 10-year-old son. They have asked that Shah be assigned to the new case.