The terrorist group made the claim of responsibility to the Irish News newspaper.
The statement came four days after her barbaric murder and just over 24 hours after the chairman of political wing Saoradh, Brian Kenna, called on the ‘New IRA’ to apologise.
In a statement given to the paper the group offered “full and sincere apologies” to her family and friends.
Ms McKee, 29, was shot in the head on Thursday night while observing rioting in Creggan estate.
The statement from the New IRA comes after Saoradh had previously sought to justify the use of violence on Thursday.
Ms McKee was standing near a police landrover when she was shot after a masked gunman fired towards police and onlookers.
A protest by friends of Ms McKee took place on Monday outside the office of Saoradh, a political group linked to the New IRA.
A number of women smeared red paint in hand prints on republican slogans outside the office.Police were present but did not make any immediate arrests.
In a statement to The Irish News, using a recognised codeword, the group admitted it was responsible for the attack.
“In the course of attacking the enemy Lyra McKee was tragically killed while standing beside enemy forces,” the statement said.
“The IRA offer our full and sincere apologies to the partner, family and friends of Lyra McKee for her death.”
The group, which formed in 2012 following an amalgamation of several dissident groups, also accused police of “provoking” the rioting that preceded the gun attack that killed Ms McKee.
“On Thursday night, following an incursion on the Creggan by heavily armed British crown forces which provoked rioting, the IRA deployed our volunteers to engage,” it said.
The statement, which was signed T O’Neill, added: “We have instructed our volunteers to take the utmost care in future when engaging the enemy, and put in place measures to help ensure this.”
Ms McKee’s funeral will take place on Wednesday, April 24, at 1 pm in St Anne’s Cathedral in Belfast.