According to CNN, a woman of the group which is an off-shoot of a Christian church in Los Angeles, said they were "perfectly OK" and were shocked and angry to learn that such an extensive search was under way.
The woman said they had been praying all night in the park and that they had done this routinely.
Steve Whitmore, a spokesman for the Los Angeles county sheriff's department, said that authorities had been scouring the Palmdale area of northern Los Angeles on horseback and by helicopter Sunday in search of the group, which included eight children between the ages of three and 17.
A resident spotted one of the vehicles identified in the lookout at a park and informed the sheriff's department, he said.
The search began Saturday, when the husbands of two women in the group reported them missing. One of the men said their wives were part of a "cult-like group" and had been "brainwashed" by its leader, Whitmore said.
A woman also left a purse with her husband and asked him "to pray over" it, the official said.
When the husband opened the purse, he found money, mobile phones and notes that "talked about meeting Jesus, talked about deceased relatives soon to meet up", Whitmore told CNN.
"The letters themselves could be interpreted in many ways," Whitmore said. "Now, some of the language in it could be interpreted as saying goodbye as relatives, but that's an interpretation." But given the husbands' concerns, "It is better to overreact than underreact," he said.
The husbands told investigators that the group had broken away from a Christian church in Los Angeles "and formed a separate group that included both traditional and non-traditional practices and beliefs", the Sheriff's Department said.