Helen Melnyk and her longtime friend, Anatoly "Tony" Nosow, told relatives and friends they would return in a few hours on Saturday.
Kristina Melnyk, the daughter of the missing woman, said she was on the phone with her mother just before the phone lost a cell signal in the remote desert.
"She was supposed to call me when they got home and she never called me," Melnyk said. "I text her, I called her, I got no response."
Park rangers on Monday began searching back roads in the hopes of locating Nosow's 2011 blue-grey Chevy Z-71 4x4 pickup truck with a license plate 32248B1
"If you find the car then you have a pinpoint location from which to organize a ground search," said Joe Zarki, a spokesman for the park. Searchers were scouring 1,200 square miles.
Friends of Nosow say the 59 year old is an avid off-roader and is familiar with the park. They said his truck was equipped with a GPS system to help navigate the desert's rough terrain.
"I've looked at all the places that he's likely to go and there is no sight, nothing," said Nosow's friend, Dave Roberts. "It's like they just vanished. I can't imagine. So, yeah, foul play has entered my mind."
As another day without her mother looms, Melnyk said she is becoming more concerned about their wellbeing.
"That they don't have food, that they don't have water, that they're cold, that I am not going to find them," she said.
Anyone with information on the couple's whereabouts was asked to call the Joshua Tree National Park Ranger Station at (909) 383-5651.