A post mortem examination is being carried out on the body of the man who died while in garda custody in Dublin early this morning.
Dwane Foster, 24, from Finglas, is understood to have been the chief suspect in the investigation into the shooting dead of mother-of-one Donna Cleary in Dublin on Sunday.
Gardaí say there is no suggestion that he was mistreated by gardaí.
On RTÉ Radio, garda spokesman Superintendent Kevin Donohue said all Mr Foster's interview sessions at Coolock Garda Station were videotaped and there was no question of any maltreatment.
Earlier, it emerged that the 24-year-old had severe health problems. He had been diagnosed with throat cancer and had sustained injuries after falling off a motorbike last year.
Labour wants independent probe
The Labour Party has called for an independent investigation into the death.
A Chief Superintendent has been appointed to investigate. However, Labour TD Joe Costello has said that this is not sufficient and that the matter should be handed over to the new Garda Ombudsman Commission.
Mr Foster was one of five people arrested in Co Kildare in connection with Sunday's murder in Coolock.
Three of the five were taken to Santry Garda Station but Mr Foster, along with another man, was brought to Coolock.
Gardaí say he complained of headaches and being unwell a number of times throughout the day yesterday and was seen and treated by a doctor three times.
He felt unwell again at around 9pm last night and was taken to Beaumont Hospital where he was treated and released back into garda custody.
However, at around 3am an ambulance was called to Coolock and Mr Foster was taken back to Beaumont Hospital where he was pronounced dead at 3.15am.
Three men and one woman are still being questioned in connection with the murder of Ms Cleary.
Ms Cleary, who was 22, was shot dead when three men opened fire on a house at Adare Green in Coolock after being refused entry to a birthday party.
Judges consider Ahern's comments
Meanwhile, judges are considering comments made following the shooting by the Taoiseach and the Minister for Justice on the sentences imposed for serious criminal offences.
Bertie Ahern promised that new laws to deal with gun crime would be in force by the end of the year. He said he wondered if sentences for serious crimes were just too lenient.
Michael McDowell said that serious drugs offences should be dealt with very severely.
Fine Gael’s Jim O'Keeffe has said the killing represents a new level of depravity. He said the tragedy confirmed that guns are readily available on the streets and that the Government has lost the fight against crime.
