Levi Bellfield claims he was offered payment by Michael Stone to confess to the Chillenden murders.
Bellfield, who is serving two whole life sentences for the murders of two women and schoolgirl Milly Dowler, denied making a confession to the 1996 killings of Lin Russell, 45, her daughter Megan, six, and the attempted murder of her other daughter Josie, then nine.
On Wednesday, lawyers acting for Stone, who is serving two whole life sentences for the hammer killings, said they had new evidence Bellfield had confessed to the Chillenden murders.
But on Thursday, Bellfield's lawyers said Stone had offered him payment to confess, and that the serial killer has had to complain to prison authorities about contact.
In a statement, his lawyer Julie Cooper said: "Mr Bellfield denies the murders of the Russell family and denies ever making such a confession.
"Mr Stone has offered payment to our client, which he anticipates receiving as compensation for time served in custody.
"Our client has three notes from Mr Stone in this regard which has been given to the prison service, together with a number of complaints regarding Mr Stone about his persistent attempts to get our client to accept responsibility for his (Mr Stone's) crimes.
"Mr Bellfield instructs that he has invited Mr Stone to undertake a polygraph test, which has been declined.
"For the record, Mr Bellfield is willing to undertake such a test in respect of the murders for which he is serving a life sentence and the murders of the Russell family."
The statement also denied specific parts of the alleged confession, and said previously unpublicised details had been reported in the media.
Bellfield and Stone are both in HMP Frankland, though are understood to be on different wings.
Nick Downing, assistant chief constable for the Kent and Essex Serious Crime Directorate, said: "We feel it is no longer contemporaneous and is unfair on the victims to continue to raise questions or re-release details about the murder investigation and subsequent conviction of Michael Stone."
The Criminal Cases Review Commission (CCRC), which dismissed an appeal in 2010, confirmed it had received an application from Stone's lawyers in August and is investigating.
A jury at Maidstone Crown Court found Stone guilty of murder and attempted murder in October 1998.
The convictions were quashed by Court of Appeal judges in 2001 after doubts over key witness Damien Daley, who said Stone confessed to the Russell murders through a heating pipe at Canterbury Prison.
However, Stone was convicted again following a second trial at Nottingham Crown Court.
Bellfield, who now calls himself Yusuf Rahim, was sentenced to life in prison without parole for abducting and killing Milly in Walton-on-Thames, Surrey, in March 2002.