Senior Pastor Mervyn Milne, of the Perth Christian Fellowship, conceded that attempts to trace him were like “finding a needle in a haystack.”
However, he said church members are continuing to search for the 65-year-old as many still feel “something good” will come out of his disappearance.
Mr Edwards, an associate pastor, who is originally from New York, moved to Scotland around 30 years ago.
Police have scoured CCTV footage of him leaving a bus in Perth on November 1. He was spotted in Aberdeen and Stonehaven the same day, but has not been seen since.
On Monday, Mr Milne said there is “strong support” in prayers for Mr Edwards.
“We’ve had hundreds of people praying for Peter in our churches and some of our affiliated members in Stonehaven have been actively searching for him at the bus station and train station up there,” he said.
“It is very much a waiting game and sometimes you think the worst. We will continue to pray through the day and every night and will do so until we get further news.
“The search for Peter is a bit like looking for a needle in a haystack but, as for the church, we all feel something good comes out of all of this.”
Mr Edwards is described as being 5ft 9ins in height, balding with a grey beard and gold rimmed glasses. He speaks with an American accent.
When last seen he was wearing a long sleeved grey shirt, black tank top jumper, tie, grey trousers and black leather shoes.
Anyone with information on Mr Edwards should phone Police Scotland on 101.