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 Londonderry’s Creggan estate.
Police say there has been a “massive response” to her killing and have urged more members of the public to come forward.
The statement from the New IRA comes after the hard-left republican political party Saoradh – which has the support of the New IRA – had previously sought to justify the use of violence on Thursday.
Ms McKee was standing near a police 4×4 vehicle 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 an office in Derry used by dissident republican political groups.
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.
Police said the public response to the killing had been “massive”.
Det Supt Jason Murphy said there had been a “palpable change” in community sentiment in support of their investigation, in terms of off-the-record intelligence.
He has urged members of the public to “come forward and have a conversation with me”.
It is understood that police and the Public Prosecution Service have discussed what measures could be available to protect witnesses fearful of giving evidence at trial.
The New IRA is believed to have been formed between 2011 and 2012 following the merger of a number of smaller groups, including the Real IRA, which itself was born out of a split in the mainstream Provisional IRA (PIRA) in October 1997 over Sinn Fein’s embrace of the peace process.
The New IRA has been linked with four murders.
Ms McKee’s killing came 21 years after the Good Friday peace agreement was signed in Northern Ireland.
The 1998 peace deal marked the end in the region of decades of violent conflict – known as the Troubles – involving republicans and loyalists during which about 3,600 people are estimated to have died.
The Good Friday Agreement was the result of intense negotiations involving the UK and Irish governments and Northern Ireland’s political parties.
Ms McKee’s funeral will be held at St Anne’s Cathedral in Belfast on Wednesday.
Her partner, Sara Canning, said the service would be a “celebration of her life”.