North East Derbyshire MP Lee Rowley says his community will be “shocked and worried” following the discovery of four bodies in a house.
Officers were called to a home in Chandos Crescent, Killamarsh, near Sheffield, at around 7.25am on Sunday.
Derbyshire Constabulary said a man has been arrested and they are not looking for anyone else in connection with the deaths.
The victims have not been publicly identified but their relatives have been informed.
Tory MP Mr Rowley described the incident as “terrible and hugely tragic”, adding: “Killamarsh is such a lovely, close knit and warm community and I know that many residents will be shocked and worried by the news.
“This is believed to be an isolated incident with an arrest having been made. I’ve no doubt that the village will pull together at this difficult time.”
Neighbours left flowers by a police cordon at the house on Monday morning. The street was sealed off and police officers remained at the scene.
A large playing field on one side of the house had also been taped off and there was a blue police forensic tent in the house’s front garden.
One man living nearby told the PA news agency: “I’m shocked. I think people will be devastated.”
The man said he believed the family who live in the house had been there for five or six months.
Detective Chief Inspector Rob Routledge, who is leading the investigation, said on Sunday evening: “We would really like to hear from anyone who saw or heard anything suspicious in the early hours of this morning, or has any information which they think could help with our inquiries.
“No matter how small you think that information may be, please do get in touch with us.
“It is understandably a worrying time for the community, and we would like to thank them for their patience and understanding at this time.
“It was important to us that close relatives of those involved were informed before we could give further details about incident.
“Residents will continue to see a large police presence in the area, and patrols are being carried out for reassurance.
“If you do have any concerns, please don’t hesitate to speak to them.”