Mr Black, a married father-of-two, was fatally shot on the M1 on Thursday morning, as he drove to work at Maghaberry Prison.
On Tuesday a funeral service will be held at Molesworth Presbyterian Church in his hometown of Cookstown, where hundreds are expected to pay their respects.
First Minister Peter Robinson and deputy First Minister Martin McGuinness both proposed to go to the service, but it is understood the Black family declined Mr McGuinness's offer.
UTV understands there will be no Sinn Féin representation at the service.
It comes after a minute's silence was held in the Stormont Assembly on Monday.
An urgent motion was proposed by the DUP leader, who told MLAs that the utmost security must be given to prison officers to try and prevent a repeat of Mr Black's murder.
Mr Robinson said the attack serves as a "timely reminder" that the terrorist threat still exists in Northern Ireland.
"The events of this last week, and in particular the murder of David Black, have been a timely reminder to all of us of the terrorist threat that still exists," he said.
"While as a society we've moved a very long way from the dark days of the Troubles, we've had a chilling reminder that we cannot afford to be complacent about the threat and ideology of terrorists.
"The fact that the acts of this nature are now so rare and the condemnation is so universal is a mark of how far we've come as a society," he added.
This morning this Assembly united, we galvanised in opposition to these terrorist acts, in support of those who have been so tragically touched by terrorism.
Justice Minister David Ford also briefed MLAs on the personal security of members of the Prison Service.
Mr Ford said the safety of Prison Service staff "is of high priority and is of course kept under constant review".
"It was a crime of the worst sort, the murder of an innocent man, cold-blooded, utterly ruthless, a defenceless man going to his work, a man who served this community well and with dedication and courage as a prison officer," he said.
"Following David Black's death, the Prison Service management responded immediately to remind staff of the need for vigilance and reissued guidance on personal security," explained the Alliance minister.
"The Prison Service also triggered and urgent review of security and a director General has today issued further advice to staff on the assessed threat level and reminding staff of the range of personal security measures which are already available to them," he added.
Paul Givan, the DUP chair of the Justice Committee, said the security of prison officers has been "a matter of concern that has been raised repeatedly before the tragic murder of David Black that officers felt their security concerns were not being treated seriously".
Mr Ford said he will meet with PSNI Chief Constable Matt Baggott on Tuesday.
"I've also had discussions with the Justice Minister in Dublin who has assured me that the necessary support which the Garda Siochana may provide will also be provided and there will be other meetings, so the matter is being treated extremely seriously," he said.
Representatives from Sinn Féin, the UUP and the SDLP also united to condemn the killing.
Mr Black, 52, is the first prison officer to die at the hands of paramilitaries since 1993.
Trade Unions will hold a silent vigil in his memory at Belfast City Hall on Tuesday. A piper will play at 1pm for the murdered prison officer.
Irish Congress of Trade Unions spokesman Peter Bunting said: "This vigil is an opportunity for all working people and their families to express their sorrow and disgust at this heinous attack on a public servant, and our collective solidarity with his family and colleagues.
"The strength of such a silent protest will be in the dignity of its participants and the simplicity of our message.
All prison visits to Maghaberry have been cancelled on Tuesday. A Prison Service spokesman said any booked visits will be rearranged.