Murder suspect Mark Hobson's mother issued a direct appeal today for her son to give himself up.
The binman's mother, Sandra Hobson, said: "The best thing you can do is contact the police."
The 34-year-old is wanted for questioning over the double murders of twins Claire and Diane Sanderson and housebound pensioners James and Joan Britton.
In the emotional appeal, Mrs Hobson said: "I've been thinking of you since I was last with you. I know things are difficult and you might be thinking about what to do next.
"Mark, the best thing you can do is to contact the police. If not the police, then a solicitor, or someone who can help you.
"Please slow down and please don't hurt anyone. There are people who can help you. Please do this for yourself and for me and the family."
North Yorkshire Deputy Chief Constable Roger Baker also revealed that evidence recovered from the two murder scenes meant that the two double murders could be "positively linked".
Scar-faced Hobson has not been seen since the killings of twin sisters Claire and Diane Sanderson, in Camblesforth, near Selby, on Sunday.
Police said forensic tests showed that Claire had been dead for a number of days before she was discovered.
But her sister Diane was seen and spoke to a number of people on the Saturday before she was found dead.
Police therefore believe that Hobson may have killed Claire at the flat they shared together and then lay in wait for her sister several days later.
It was also revealed that there were problems in identifying 27-year-old Claire because her body was decomposing when it was found.
Detective Superintendent Javad Ali, who is leading the two double murder investigation, also revealed that Claire had not been seen since July 2.
He said: "We believe she was last seen on July 2, but we have got other sightings that we are investigating.
"We believe Claire had been dead for a number of days but we don't know how long she had been dead."Reuse content