Nicola Bulley's two young daughters reportedly "cried their eyes out" when their dad had to explain to them that their mum was lost.
She went missing last Friday morning, with her mobile phone found on a bench near to where she was last seen on a towpath by the River Wyre in St Michael's on Wyre, Lancashire.
Immediately before disappearing, Ms Bulley was walking her dog, springer spaniel Willow, who was found loose between the river and bench.
Nicola's partner Paul Ansell reportedly had to tell their children about what had happened, and her mum Dorothy revealed: "He just said 'mummy's lost."
The Sun reports that his dad David added: "They cried their eyes out."
Mum appeared 'completely normal' moments before vanishing while walking dogPolice have said they are keeping an "open mind" about what happened, but do not believe Ms Bulley was attacked.
In a statement, her family said: "We have been overwhelmed by the support from our community and would like to thank everyone for their ongoing efforts to help us find Nicola.
"The girls are desperate to have their mummy back home safe with them and your ongoing efforts have provided comfort to them whilst we await news on Nicola.
"We ask for anyone who thinks they may have any information that may help the police find Nicola to please come forward and help them with their inquiries."
A search of the area involving police specialist resources, the Coastguard and Bowland Mountain Rescue is continuing.
Ms Bulley is described as white, 5ft 3in, with light brown, shoulder-length hair.
At the time of her disappearance she was wearing a long black gilet jacket with a hood, black jeans and olive green ankle wellington boots.
Superintendent Sally Riley said: "We remain extremely concerned for Nicola and we continue to do everything we can to try and find her and to provide some answers for her family, who are obviously beside themselves with worry.
"I must stress at this time that this remains a missing person inquiry and at this time there is nothing to suggest any third-party involvement in Nicola's disappearance.
"We appreciate there is also a great deal of concern in the local community, and we appreciate people want to help. However, parts of the riverbank are treacherous, and we would ask that nobody puts themselves in danger and that the police and partner agencies' efforts to find Nicola are not compromised.
Devastated parents promise to never stop looking for mum-of-two who vanished"If anybody has any questions or concerns, they are welcome to speak to officers in the area."
Anyone who has seen Ms Bulley, or has information about where she might be, is asked to call 101, quoting log 565 of January 30, or call 999 if they have an immediate sighting.