Halsey said on Twitter that he had "seen an incident and been told to say I haven't seen it".
He spoke out after Manchester City's Sergio Aguero received a retrospective three-game ban for violent conduct.
However, the Professional Game Match Officials Limited said: "There is no pressure to include or omit anything."
The body's statement continued: "Match officials submit their reports, including critical incidents, directly to the FA.
"Match officials ensure that their reports are a full and accurate description of the incident."
Halsey, who retired in 2013, also pointed out these were issues he had previously mentioned in his autobiography three years ago.
He later added: "To be fair to the FA... it's not them, it comes from within the PGMOL."
Formed in 2001, the PGMOL was established when referees turned professional and aims to improve standards across the Premier League, Football League and FA competitions in England as well as training and development.
Had the incident that saw Aguero banned by a Football Association panel for elbowing West Ham's Winston Reid been witnessed by a match official, including referee Andre Marriner, the retrospective punishment would not have been possible.
Former Manchester United captain Gary Neville said Halsey's claims were "too big" to avoid a full investigation.
Former referee Mark Halsey's claims that he was told to lie after a game have been denied by the body which oversees match officials.