A team of 10 senior detectives has been sent to Offaly to investigate new evidence in the murder of Fr Molloy in 1985.
Det Supt Christy Mangan said last night that the probe was taking place as a result of information given to gardai by the Irish Independent. Officers from the Garda National Bureau of Criminal Investigation have been assigned to the case.
The newspaper has been involved in a two-year investigation into the killing of the Roscommon priest, who was beaten to death in the Clara mansion of his socialite friends Richard and Therese Flynn in July 1985.
The post-mortem found the 52-year-old had been punched and kicked in the head at least five or six times and died as a result of severe head injuries.
Mr Flynn was charged with manslaughter, but the trial collapsed after three hours when Mr Justice Frank Roe directed the jury to acquit him.
It later emerged that the judge knew the parties involved and should not have heard the case.
In the midlands, it is widely believed that another individual, not Richard Flynn, murdered the priest.
The probe revealed new evidence that other people were present in the house on the night of the killing, including a Fianna Fail politician who was a household name.
It also emerged that a Kilkenny surgeon related to the Flynns was present on the evening of the murder, too.
He later admitted to a friend that the events of that night had left his life in ruins. Shortly afterwards, he died suddenly at the age of 50.
New medical evidence obtained shows Fr Molloy did not die instantly, but was left for up to six hours after the initial attack before gardai were called.
Three leading pathologists have stated that his life could have been saved.
Last night, Fr Molloy's family expressed relief at the new development but said they would not rest until their uncle's killer was brought to justice.
The priest's nephew, Bill Maher, said: "For 27 years we have been deprived of justice and the truth for our uncle Niall, a man we all adored and who is still loved and remembered fondly by his parishioners in Roscommon. His killer has been allowed to walk the streets for almost three decades. We know that many people have information about Niall's murder and we are urging them now to come forward and help the gardai with their inquiries so that justice can finally be done."