Sara Canning said an apology was meaningless while the group continues to shielded the person responsible for killing the 29-year-old.
While a number of people have been arrested in connection with the murder in Derry last April, no charges have been brought.
The New IRA first apologised for the murder in Creggan during which the journalist was killed while observing rioting in the area.
She died after being struck by a single bullet to her head.
Police officers rushed Lyra to Altnagelvin Hospital in an armoured PSNI landrover but she was later pronounced dead from the catastrophic injury.
Ms Canning said every word uttered by the group rings hollow.
“Lyra is dead because of your actions, and it’s a wonder more lives weren’t lost that night. Give up the murderer, and give up in general. You’ve admitted your actions won’t yield a result you want.
“Stop using Lyra’s name to try to evoke some sort of positive response, you bring nothing positive, you’re a stain on our society, and the lives you have taken are unjustifiable,” she said.
The statement, sent from terror group to the Irish News, said: “The IRA again take this opportunity to offer our full and sincere apologies to the partner and family and friends of Lyra McKee for her death.
“Our volunteers have been instructed to take the utmost care in future when engaging the enemy and we have put in place measures to ensure this.”
The group also said they would “meet force with force” in reference to the security forces.
“Against a background of the British government and its proxies stamping their authority on Ireland by force, we in the IRA intend meeting force with force,” they said.
It comes just a few days after Ms McKee was posthumously awarded a Master of Arts degree in online journalism by Birmingham City University, where she previously studied for a distance learning master’s degree.
Ms Canning, writing on Twitter, said it’s “unfair” the group made their renewed apology after Ms McKee received the award.
“She had plans to go back and finish that masters after Lost Boys, there were plans and dreams and a life that she had planned for herself, and it was snatched away by these morons,” she said.“The same for the others whose lives have been taken and for what? Absolutely nothing, their aim will never be realised, what they claim to ‘fight’ for is not the will of the vast majority here.
“The future of this place is uncertain, but it will never be what they envisage.”
On Wednesday, the representative body for police officers in Northern Ireland branded the apology as “hollow”.
“Hollow words from terrorists,” the Police Federation tweeted.
“The only way to ensure this never happens again, is to disengage from trying to murder ANYONE and accept that the overwhelming majority of people want to live in peace.”
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