Lynn and Barry Collett, who were married in Hampshire on Saturday, were last seen leaving their holiday cottage in the Dales on Monday, North Yorkshire police said.
The alarm was raised after a member of the public spotted a man's body in the river Wharfe at Bolton Abbey, near Skipton.
After recovering a red jacket with the couple's address police turned up at the deserted holiday cottage in the village of Appletreewick to find the living room filled with wedding presents, cards and even a tier of wedding cake.
As the search, using police divers, the Upper Wharfedale Fell Rescue Service and workers from the Bolton Abbey estate, entered its fourth day yesterday, police said hopes of finding the couple alive were fading.
Chief Inspector Ron Johnson said: "We are investigating what we believe is very probably the drowning of a newly married couple on the second day of their honeymoon.
"Clearly, with every passing day, hope is giving way to the belief that the couple have met with a terrible accident and drowned together in a treacherous stretch of water. We continue to hope for the best. We fear the worst."
The couple vanished at a notorious stretch of the river Wharfe, known locally as the Strid, said to be riddled with underwater pools, hidden ledges and powerful undercurrents. It is flanked by warning signs and on the day of their disappearance it was swollen with rainwater. Further rain fell on Monday night making it too dangerous for searches to start until yesterday.
The couple's parents have travelled to the area and are being cared for by specially trained police officers.
Mrs Collett, whose maiden name is Spreadborough, comes from Hook in Hampshire. She was a student nurse and Wednesday would have been her 26th birthday. Her 29-year-old husband works as a computer operator for an engineering company and comes from Camberley, Surrey.
The couple were married on Saturday in the village of Long Sutton in Hampshire.
They spent their wedding night at a hotel in Maiden's Green, Berkshire, before travelling to their holiday cottage by car on Sunday.
The spot where the couple are believed to have fallen in is about one- and-a-half miles from the holiday cottage, where they were last seen.