Story highlights Kelli Abad disappeared the night that she and her husband argued, he says

She has been missing for six weeks

Her car is found near cliffs on the island of Okinawa with a note inside

Her family is holding out hope but is aware of the possibility she's gone

The husband of an American woman, who has been missing for six weeks in Japan, said Thursday that she had threatened to kill herself the night she disappeared after the two argued.

Vince Abad, an airman at a major U.S. Air Force facility in Japan, said he and his wife, Kelli, had fought over the phone on the night of October 26 after he had gone to see their pastor, who had helped resolve disputes between them in the past.

When he returned home, his wife was gone and their two children were in bed.

"We'd had arguments before -- it didn't feel too out of place," Abad, 30, said. He said he assumed she had gone to stay with a friend.

But when Kelli Abad, 27, didn't come back by the following morning, he became concerned and raised the alarm.

Two days later, the wife's car, a Toyota SUV, was found at Cape Zanpa on the island of Okinawa, about 10 miles from the base, with her cell phone and purse inside.

Also inside the car was a note, Abad said, that read, "Love my kids, love my hubby and parents. Bye."

Cape Zanpa is known locally as a place for committing suicide, Abad said.

The Japanese police, the fire department and coast guard have searched caves and cliffs in the area but have found no trace of her, the police have said. The U.S. military has been helping with the search.

Family members have also attempted their own searches in the area, he said.

No witnesses have come forward, despite a poster campaign in English and Japanese saying she is missing.

The family is "always hoping for the best -- that she's out there," Abad said. But they are also aware of the possibility that his wife "might have decided to leave us on her own terms."

"Right now, she's a ghost," he said.

The couple's two young children -- a 1-year-old boy and a 4-year-old girl -- are learning to deal with their mother's absence, Abad said.

In the first few weeks after Kelli Abad's disappearance, he found his daughter crying one night. When he asked her what was wrong, he said, she replied, "We don't have a mommy."