An 86-year-old woman who was killed in a "horrific" attack at her home in Langwith Junction, near Mansfield, has been named as Freda Walker.
Her husband, local politician Ken Walker, 88, was taken to hospital with life-threatening injuries for treatment where he remains in a critical condition.
Derbyshire Police have launched a manhunt and have yet to make an arrest.
'This has sent shockwaves through the community'
Council leader, Steve Fritchley said the entire community had been left shocked.
He said: "It is terrible when something like this happens, but it really hits home when it happens on your doorstep and to someone you know.
"It’s very upsetting and I was quite angry over the weekend. Ken and Freda were in their own home, a place where everyone deserves to be and feel safe, only to be attacked and ultimately bringing Freda's life to a premature end.
"We have heard many people say, 'Ken and Freda, what a lovely couple' and they really were. This has sent shockwaves through the local community."
He said Mr Walker was an "example to all" and Mrs Walker was "lovely".
He added: "Just when they should both be enjoying their twilight years together, this terrible incident has happened and our thoughts are with Ken and his family."
Local residents in Langwith told ITV News that the attacks were "horrific" and that Freda and Ken were a lovely friendly couple.
One person said that it was "unimaginable" what had happened and that there were no words for what those responsible had done.
Police were called by paramedics at 9.30am on Saturday, 15 January, to reports that a man and a woman had been found with serious injuries at a house in Station Road.
Derbyshire Constabulary has confirmed that officers will remain at the property for some time.
Divisional commander, Chief Supt Hayley Barnett, said: "This is a horrific incident for the community of Langwith Junction and our thoughts remain with the family and friends of those affected.
"The family of the couple have been made aware and are being supported by specialist officers.
"We would ask that their privacy is respected at this time."
She said residents would see extra police and "all force resources", along with the East Midlands Special Operations Unit, were working on the case.
"While the investigation is in its early stages, I can confirm this is not being treated as a domestic incident.
"There was also a serious level of violence used in the incident and we are doing all we can to understand the circumstances and find those responsible."
She urged people to take extra precautions at home, saying: "Keep... doors and windows locked, don’t let any strangers in, don’t keep any valuables on display and have a means of making contact with emergency services."
Anyone who may be able to help detectives with their enquiries is asked to contact Derbyshire police using any of the below methods, including reference 240-1501