In a statement given to The Irish News using a recognised codeword, the group offered “full and sincere apologies” to her family and friends.
Ms McKee was standing next to a police car on the Creggan estate when she was hit as a masked gunman fired towards police on 18 April.
Police believe the violence was orchestrated in response to an earlier search by officers aimed at averting imminent trouble associated with this week’s anniversary of the Easter Rising.
The New IRA is an amalgam of armed groups opposed to the peace process. It recently claimed responsibility for parcel bombs sent to London and Glasgow in March.
The group said in a statement: “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.
“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.
“In the course of attacking the enemy Lyra McKee was tragically killed while standing beside enemy forces.
“The IRA offer our full and sincere apologies to the partner, family and friends of Lyra McKee for her death.”