The 66-year-old appeared in connection with the murder of two Ulster Defence Regiment soldiers in County Fermanagh in 1972.
Downey was detained by Gardai on Monday evening under a European Arrest Warrant as part of a joint operation with the PSNI.
It comes as Northern Ireland prosecutors seek to extradite him to face charges of murder.
Detective Sargent Jim Kirwin of the Garda Extradition Unit told the court that he was on duty in Donegal when he spoke to Downey at a house in Ards, Creeslough, on Monday.
The garda officer asked Downey his name and told him that he was the subject of a European Arrest Warrant.
Downey responded that it was the "DUP and not the DPP (Director of Public Prosecutions)" who was pursuing the matter.
The officer told the court that the warrant related to three offences including a bomb in Co Fermanagh in 1972 which killed the two UDR members.
The officer confirmed that Downey's passport has been surrendered to gardai and when asked by a prosecution barrister if he co-operated with police, the detective replied: "Fully, Judge."
His defence barrister confirmed that Downey is contesting the application and is "anxious to get bail".
He added that his client suffers from a medical condition and has a heart monitor fitted.
He then asked the judge to consider an early date for a bail application.
His bail application will take place on Thursday at the Criminal Courts ofJustice.
The extradition hearing will take place on Friday, November 23.
Prosecutors in Northern Ireland have decided there is sufficient evidence to prosecute him for the murders of Lance Corporal Alfred Johnston, 32, a father-of-four, and Private James Eames, 33, a father-of-three, in Co Fermanagh.
They died when an IRA bomb exploded in a car they were checking on the Irvinestown Road, Cherrymount, Enniskillen on August 25, 1972.
In 2013, Downey was charged with murdering four Royal Household Cavalrymen in a bomb in London's Hyde Park in 1982.
He stood trial at the Old Bailey, but the case dramatically collapsed after it was revealed he had received a written assurance from former prime minister Tony Blair's government that he was not actively wanted by the authorities.
The letter was issued under the terms of the controversial On The Runs (OTRs) scheme.
The episode sparked a government inquiry into the scheme.
Mr Downey has always denied any involvement in the Hyde Park attack.
A number of supporters including three Sinn Fein TDs, Pearse Doherty, Sean Crowe and Dessie Ellis, were also in court for Tuesday's proceedings.
Speaking outside court, Mr Doherty said: "In my view this arrest was wrong. It shouldn't have happened and in my view John should be returned to his family where he has been living for the last number of decades.
"I think everybody is entitled to justice and I deeply regret any suffering and loss that has happened because of the conflict but that doesn't take away from the fact that John Downey has been arrested on the first occasion despite having assurances that he was not wanted for questioning in relation to any incident.
"That arrest took place after a long protected period of time.
"It is deeply concerning that John has been arrested. It won't be lost on anybody that this has happened at a time when the British Government and authorities are looking for a blanket amnesty for their own soldiers given the spotlight is on them for their activities in the north."
Sinn Fein MLA Gerry Kelly has said that Downey's arrest was an act of "gross bad faith".
"John Downey has been a supporter of the peace process over many years and to pursue his arrest and extradition now is vindictive and bad faith.
"It gives lie to claims by British Prime Minister Theresa May that the legacy process is skewed against former state forces.
"This false assertion is motivated only by a desire to secure immunity and impunity for British state forces guilty of crimes in Ireland."