At Commons question time, Mr Blair said the killers were "not loyal to anything other than their own bigotry and prejudice, and that is not a loyalty shared by any sensible member of the United Kingdom".
He said the killers were "trying to wreck the hopes of peace for the vast majority of people in Northern Ireland".
He spoke as the Chief Constable of Kent was due to arrive in Ulster to begin his investigation into the brutal murder.David Phillips was asked to lead the sensitive inquiry after the Chief Constable of the RUC, Sir Ronnie Flanagan, said he wanted the investigation to be transparent and seen to be so. Mr Phillips will oversee the investigation, in which the FBI is also being given a role.
Sir Ronnie said he thought it important for the Nelson family to know that "not only will this investigation be meticulous, but that it will be transparently obvious to them and the watching world as such".
The decision to bring the FBI into the Nelson investigation follows long-standing police links between Dublin, Belfast and Washington. Sir Ronnie initiated the idea soon after Mrs Nelson's death, and he discussed it very early the next morning with Mo Mowlam, the Secretary of State for Northern Ireland, who had just arrived in Washington.
It was prompted by the personal friendship between Sir Ronnie, the Garda Commissioner Pat Byrne and the FBI director Louis Freeh. Both Sir Ronnie and Mr Byrne attended the FBI's National Academy,an 11-week training programme for police managers from the US and around the world, and its National Executive Institute. Policemen from the RUC and the Garda Siochana also attended a special training programme earlier this year at the FBI Academy in Quantico, Virginia.
The FBI would not comment on its role in the Nelson investigation yesterday. British officials said it was much too early to say what assistance the FBI might provide.
A group called the Red Hand Defenders has claimed responsibility for the car bomb which killed Mrs Nelson, leaving her husband and three children devastated.
Her two sons were brought home early from a school skiing trip in France to be with their father and sister for today's requiem mass at St Peter's Church, Lurgan, followed by a cremation at Roselawn, East Belfast.
Vigils for Mrs Nelson were held last night in Lurgan, Londonderry and Armagh, and more vigils and demonstrations are planned. Meanwhile, the RUC has issued a fresh appeal for information about the murder.
Mrs Nelson's murder and yesterday's shooting of the loyalist paramilitary Frankie Curry heightened anxiety at Westminster over the peace process and the 29 March deadline for making progress on the Northern Ireland assembly.
Some senior politicians are privately convinced that the peace process will collapse. "It's deadlocked and is falling apart," said one Ulster Unionist MP.
But those close to Mo Mowlam said she was sticking by her call for strong nerves in the run-up to the deadline.