"We are reaching a state of emergency. We need immediate assistance," said one tweet, adding that it was also carrying a body bag containing the corpse of one migrant who had died.
The better part of the migrants in all the districts, except for in the West Bank, come from other areas within the same district.
"Discrimination and attacks are now added to existing threats like gang violence that drove these children to leave in the first place," UNICEF Executive Director Henrietta Fore said.
Under the law until now, part of migrants' salaries were held in deposit by the state and given back to them if and when they left the country.
About 60,000 people have been sent back to Mexico to await the outcome of their cases in often dangerous border towns.
Court to decide how far to push the government
The American Civil Liberties Union estimated that more than 5,400 migrant children are currently in government custody, and separated from their families.
sraeli law does not include jus soli – a rule that the citizenship of a child is determined by the place of its birth.
The migrants, mostly from Central and West Africa, had been drifting around 50 miles off the Libyan coast for nearly 24 hours when they were picked up.