Lyra McKee's partner described the comments from Saoradh as "absolutely appalling".
The leader of a party believed to be the political wing of the New IRA has said that a continuation of violence in Northern Ireland is "inevitable".
Brian Kenna, who is the chairman of Saoradh, told Sky News that the murder of journalist Lyra McKee in Londonderry by a New IRA gunman was "regrettable" but denied any knowledge of the gunman responsible for the 29-year-old's death.
Mr Kenna, who is a convicted IRA member who was jailed for 10 years for his part in an armed robbery, said: "The death of Lyra McKee was a very tragic event. It genuinely came about because of the heavy presence of the PSNI, flooding into Derry at seven o'clock in the evening, into parts of the Creggan."
"It was shocking and tragic and we're on record as saying that we regret that death very, very much," he added.
When asked if he knew who the gunman was, Mr Kenna said: "No, I've no idea of the events of that night."
Lyra McKee's partner Sara Canning said Mr Kenna's statement was "absolutely appalling".
Posting on social media, Ms Canning said: "They proved the police’s reason for being there by bringing a gun onto the streets and putting lives in danger, and ultimately murdering the love of my life. Had no gun come out they could have claimed unfair oppression, instead they totally justified the police presence.
"They murdered Lyra, and put many more lives in danger. It was not an accident, it wasn’t just regrettable, it was despicable. The blatant disregard for the people of the town and beyond is staggering. No lives should have been lost that night. There is no justification for murder.
"The police inside that vehicle did not deserve to die, they also did not deserve to have to fight in vain to save Lyra’s life. They did something heroic that night, which is something that no Saoradh or New IRA person can ever say. Cowards every one of them. Sickening cowards."
However, Mr Kenna said that young Irish people have always taken up arms and that this will continue.
"I believe that it's inevitable," Mr Kenna said.
"It will always happen so long as the country is artificially divided and held by force of arms, people will always strike out against that occupation," he added.
Mr Kenna continued: "If young people in the six counties have been more politicised and in some sense radicalised by events of recent times, then what's wrong with that?"
Lyra McKee was fatally shot during rioting in the Creggan area of Derry. The New IRA has admitted responsibility for her death.
Saoradh denies that it is the political wing of the New IRA.
Mr Kenna denied any overlap in the leadership of Saoradh and the New IRA and refused to condemn violence carried out by the dissident republican group.
The New IRA detonated a bomb in a car outside Londonderry Courthouse in January and attempted to kill police officers in booby-trap bomb attack in Co Fermanagh earlier this month.
Stephen Martin, deputy chief constable of PSNI, told Sky News that he has no doubt about the link between Saoradh and the New IRA.
"There are people who are members of Saoradh who are members of the New IRA and some of them are in leadership positions in the New IRA," he said.
"So there is that inextricable link between the two organisations," he added.
Mr Martin said there has been an increase in New IRA activity this year and that there was six attempts to kill police officers last year.
"Four of those incidents were very determined attempts to kill police officers… but violence isn't inevitable, nor is it excusable."