Detective Chief Inspector John Caldwell remains critically ill after being shot a number of times at a sports centre in Omagh on Wednesday night.
He has suffered life-changing injuries, according to Liam Kelly, chairman of the Police Federation which represents rank and file officers.
A fourth man was arrested overnight in the attempted murder investigation.
The 22-year-old was arrested in the Coalisland area in the early hours of Friday morning.
Three men aged 38, 45 and 47 also arrested in Co Tyrone remain in custody.
The leaders of the five main parties at Stormont will meet PSNI Chief Constable Simon Byrne at police headquarters in Belfast on Friday morning to discuss the attack.
They issued a joint statement on Thursday in a show of unity against those responsible.
Sinn Fein vice president Michelle O’Neill described the shooting as an “attack on the peace process”.
Gunmen shot Mr Caldwell in front of his young son in the attack at the Youth Sports Centre.
He ran a short distance and fell to the ground where the attackers continued to fire at him as children ran in terror to get to safety, police said.
The dissident republican group the New IRA is the “primary focus” of the PSNI’s attempted murder probe.
The attack has been condemned by political leaders across the UK and Ireland.
Mr Caldwell was coaching a youth sports team at the facility on Wednesday evening.
Mr Byrne said on Thursday: “Clearly as an organisation we are utterly shocked and angered by last night’s brazen and calculated attack.
“John is a father, husband and colleague, and a valued and active member of his local community.”
He said Mr Caldwell has been a valued police officer for 26 years “committed to public service as a senior investigating officer supporting victims and their families in bringing offenders to justice”.
Mr Byrne added: “John is held in the highest esteem within our organisation. He is a credit to his family and to the police service.
“And of course our thoughts are with John and his family as he fights for his life in hospital today.”
He added: “This has sent a huge shockwave across the organisation.
“We’ve been speaking principally with the Police Federation but also with those representatives of senior officers and police staff who would see themselves under threat.
“Clearly, one of the things that defines us is our resilience and our commitment to keep going in dark times and tough times.
“So John knows that his colleagues will now be working tirelessly around the clock to support his recovery but also to bring the offenders that have tried to kill him to swift justice.”
Assistant Chief Constable Mark McEwan said there were “many other young people, children” waiting to be picked up by their parents when the attack on Mr Caldwell took place.
“And those children ran for cover in sheer terror towards the centre,” he told reporters.
Mr McEwan said: “The two gunmen, who were dressed in dark clothing, carried out this cowardly attack and left the scene on foot. At least two other vehicles were struck by their volley of shots.
“We believe the gunmen fled the scene in a small, dark-coloured vehicle shortly after 8pm. We believe this vehicle was abandoned and set on fire in Racolpa Road, Omagh.
“We want to hear from anyone who was in the area or who witnessed what happened to get in touch with any information that could help with our investigation.”
Mr Caldwell is a high-profile officer who has led a number of major investigations, including taking a leading role in the murder probe following the killing of Natalie McNally in Lurgan in December.
Irish police are working closely in co-operation with their counterparts in the PSNI and have intensified patrols.
The New IRA has been blamed for the killing of journalist Lyra McKee in Londonderry in 2019.
Last November, the group was also thought to be behind the attempted murder of two police officers in a bomb attack in Strabane, Co Tyrone.
Omagh has seen significant dissident violence in the past, including a Real IRA bomb attack in 1998 which killed 29 people – one of whom was a woman pregnant with twins.
It was also where Constable Ronan Kerr was murdered in April 2011.
The terrorism threat level in Northern Ireland was lowered from severe to substantial for the first time in 12 years last March.
