Customs and Border Protection in Arizona "is prepared to and expects to continue processing unaccompanied children from South Texas," said Victor L. Brabble, a spokesman for the agency in Tucson.
The Homeland Security official said that the children would be moved out of the Nogales site as soon as Health and Human Services finds places for them.
But the official said: "As quickly as we move them out, we get more. We believe this is just a start."
The children being held in Nogales are 17 or younger. The official estimated three of every four were at least 16.
Nogales Mayor Arturo Garino visited the facility Saturday, but he did not get inside the site where the children were being held. Garino said he did meet with Border Patrol officials. He was told some of the children are as young as 1 year old.
"I have all the faith in the world as mayor and as a citizen of Nogales that our Border Patrol is doing the best and the most kind and humane thing with the children," Garino said.
The town has begun collecting clothing donations for the kids, he said.
"Border Patrol has always been good to the city of Nogales, and they work very closely with us," Garino said. "Now, as a city, we need to help Border Patrol so that they can accomplish their goal of making sure these children are all taken care of."
Immigration officials can immediately return Mexican immigrants to the border, but they are much more hard-pressed to deal with Central American migrants who illegally cross into the U.S. In recent months, waves of migrants from nations south of Mexico have arrived in Texas.
The Homeland Security official said that legally, only their parents or guardians can take custody if the government makes the children eligible for release.
Officials in Central America and Mexico have noticed a recent increase in women and children crossing the border. Father Heyman Vazquez, the director of a migrant shelter in Huixtla in the southern Mexico state of Chiapas, said he and others advise children that it's too dangerous.
Yet Vazquez is seeing more and more youths heading north.
"I remember a little boy of 9 years old and I asked if he was going to go meet someone and he told me 'No, I'm just going hand myself over because I hear they help kids,' " Vazquez said.
Spagat reported from Tijuana, Mexico. Associated Press writers Alicia A. Caldwell in Washington, Bob Christie and Terry Tang in Phoenix and Maria Verza in Mexico City contributed to this report.