Ann Widdecombe was attacked nearly 24 hours before she was found dead, police believe.
The 78-year-old former Conservative minister was found with serious injuries at her home in Haytor, Devon at 11:40 BST on Thursday.
Devon and Cornwall Police said they believe the attack took place on Wednesday at around 12:30 BST, and added that enquiries were “moving at pace for a suspect who is believed to be a white male”.
On Saturday morning, the force announced a 26-year-old white British man, who had been arrested a day earlier on suspicion of murdering the former MP, had been released from custody and was “no longer part of the investigation”.
Assistant Chief Constable Matt Longman said the priority “remains identifying those responsible and ensuring that all available evidence is thoroughly examined”.
Detectives were continuing to carry out “numerous enquiries” and the investigation was “moving at a significant pace”, he added.
“We are deploying all of the necessary resources to find out exactly what has happened. I would appeal to anyone who may have information about this incident, however insignificant it may seem, to come forward and speak with us.”
Later on Saturday, Longman said the force had decided not to release further information, including descriptions of any potential suspects or CCTV footage, for the time being.
“Releasing such information prematurely could compromise ongoing enquiries and may prejudice future investigative opportunities,” he said.
A significant police presence remained in the area on Saturday, with forensic officers seen arriving at the property. People, including Reform UK leader Nigel Farage, were also seen laying memorial flowers near Widdecombe’s home.
During a police press conference on Friday, Longman said the force had ruled out terrorism and had no information to believe Widdecombe’s death was a “politically motivated crime”.
He added that it was too early to comment on whether or not the suspect was known to her.