Missing children found safe, mayor says

Two children who had been missing since Sunday in Jacksonville, Florida have been found safe, the city's mayor said.

Braxton Williams, 6, and his sister Bri'ya Williams, 5, disappeared Sunday morning after they had been playing outside their residence in the Paradise Village mobile home community, according to the Jacksonville Sheriff's Office.

"They're alive and they're well and it's amazing!" Chastity McCrary, the two children's cousin, told ABC News outside UF Hospital Tuesday afternoon.

The two were found safe Tuesday afternoon, Mayor Lenny Curry tweeted.

"The children were located in some sort of small pump house, according to the officers that located them," Jacksonville Sheriff Mike Williams said. "All indications would lead us to believe the children walked away from the home."

It's unclear how long the children were in the dilapidated pump house, but they were not trapped, authorities said.

When the children were found they were happy and talkative, Williams said. The rescuers gave them a bottle of water and candy. They asked for pizza so personnel chipped in and got them pizza, officials said.

"This is a Christmas miracle," Curry wrote.

"It was so exciting and I'm just ready to see them," said McCrary, who was involved in the search. "I said, 'Merry Christmas and Happy New Year! This was a beautiful ending to a terrible beginning."

The parents cooperated the whole time and no charges are expected.

T.K. Waters, the sheriff's office chief of investigations, said earlier in the day authorities were searching for a vehicle that had been playing loud children's music in the neighborhood where the children went missing.

He said he didn't know of a connection between their disappearance and the vehicle, but asked the community to keep an eye out for it.

The Florida Department of Law Enforcement issued an Amber Alert for Braxton and Bri'ya, describing them as "endangered."

ABC News' Victor Oquendo and Morgan Winsor contributed to this report.