Their statement comes after the New IRA admitted responsibility for Ms McKee’s death saying she was “tragically killed while standing beside enemy forces”.
The statement said that the armed group “instructed our volunteers to take the utmost care in future when engaging the enemy”.
The 29-year-old journalist died after being shot in the head during rioting in Derry’s Creggan estate last Thursday.
Following the New IRA statement her friend Sinead Quinn said the apology didn’t change the “intolerable” time experienced by Lyra’s family and friends since her murder.
“It gives no one comfort and in fact the way their statement continued on, which is basically ‘we’re not going to go away’, that flies in the face of the apology,” Ms Quinn told UTV.
“So an apology without actually positive action means nothing.”
SDLP leader Colum Eastwood said that the apology was insincere and showed a “lack of humanity” towards Lyra and the entire community of Derry.
“This morning’s statement from the New IRA is an absolute disgrace and shows no remorse for the death of Lyra McKee,” the Foyle MLA said.
“Their so called instruction to their ‘volunteers’ to ‘take the utmost care’ when engaging in violence is utterly sickening and devoid of any humanity.
“They must recognise the glaringly obvious fact they are not wanted by the people of the North.
“It is time to disband.
“The murder of Lyra McKee must not be in vain. Together, political leaders must come together to re-engage in a talks process to fill the vacuum that currently gives groups like this too much oxygen.”
UUP leader Robin Swann said that the attempt at an apology was “beneath contempt” and called on the PSNI to take action against the group.
“Their ‘full and sincere apologies’ are of no use or comfort to anyone. And to try to imply that Lyra somehow contributed to her own death because she was ‘standing beside enemy forces’ shows their tenuous grip on reality,” Mr Swann said.
“I doubt these fanatics’ pledge that they have instructed their untrained teenagers ‘to take the utmost care in future when engaging the enemy and put in place measures to help ensure this’ will provide much reassurance to anyone.“This gang needs to be rejected by all. They then need to be rounded up and put behind bars and out of business.
“There should be no pandering to them or their so-called political representatives.
“For the sake of society here they must be closed down permanently.”
A funeral service for Lyra will take place at St Anne’s Cathedral in Belfast on Wednesday, April 24, at 1 pm.