The First and deputy First Ministers presented a united front at Stormont Castle on Thursday, just hours after details of the fatal attack on the M1 motorway emerged.
"At this time, our thoughts and prayers are with the bereaved family and we condemn this murder in the strongest possible terms," Peter Robinson and Martin McGuinness said in a joint statement.
"There can be no justification for this brutal attack as this man was going about his daily life."
Mr Black, 52 and from Cookstown, died after his car left the M1 motorway when gunmen opened fire on it as he made his way to work at Maghaberry.
After more than 30 years' service, he had been nearing retirement.
The Stormont leaders added: "Actions like this have no place in society and those who carried out this murder have nothing positive to contribute, and we refuse to let the people behind this attack divert us from building a better and peaceful future for everyone.
"We appeal to anyone with any information on this murder to contact the PSNI."
Prime Minister David Cameron has also condemned the fatal attack.
"These killers will not succeed in denying the people of Northern Ireland the peaceful, shared future they so desperately want," he said.
People who work for the Prison Service play a crucial role in our community and any attack on them is an attack on all of us.
The gun attack comes less than 24 hours after Secretary of State Theresa Villiers told a Westminster committee that dissident attacks in Northern Ireland had fallen by 20% so far this year.
It is also a week after the threat of attack in Great Britain was downgraded to moderate.
"I utterly condemn this cowardly and evil attack," Ms Villiers said on Thursday.
"The thoughts and deepest sympathy of us all are with the family, friends and colleagues of the murdered prison officer.
"Like his colleagues, he was dedicated to serving the whole community in Northern Ireland - in stark contrast to the people responsible for this despicable crime."
She added: "The British and Irish Governments, the Executive, the PSNI and Garda - and above all the people of Northern Ireland - will continue to work together to ensure that those who pursue their aims by violence will not succeed."
Speaking while on an official visit to Berlin, Irish Taoiseach Enda Kenny said: "I utterly condemn the actions of those who carried it out and their scant regard for human life.
"I wish to extend my deepest sympathy and those of the Irish people to the family of the victim and to his colleagues.
"Those who committed this brutal act will rightly be condemned by all civilised and right-thinking people on this island who utterly reject such hideous and mindless violence."
Tánaiste Eamon Gilmore also extended condemnation and condolences from across the Irish border.
"I know that I speak for every decent man, woman and child on this island, north and south, in expressing revulsion at this act," he said.
"There will be no return to the dark and violent days of the past.
"The tragic loss of life that we have seen this morning serves only to bring us together in a shared grief and a shared determination to work together in building a better future for all."
Irish Justice Minister Alan Shatter added that An Garda Síochána would fully support the PSNI in "bringing the perpetrators of this dreadful crime to justice and dealing with the threat posed by anyone behaving in this barbaric fashion".
In the House of Commons, DUP North Belfast MP Nigel Dodds raised the issue of the fatal attack.
"This dastardly murder highlights that the battle against terrorism and the fight for peace and democracy continues in Northern Ireland," he said.
"Next week marks the 25th anniversary of the Poppy Day massacre in Enniskillen. Sadly, there are still people who want to plunge Ulster into the darkness and depths of despair and death.
"They must not be allowed to succeed anyone with information must help the police track down these killers and bring them to justice."
The thugs who plunged his family into despair are flat-earth fanatics living in the dark ages, spewing out hatred from every pore.
Sinn Féin Upper Bann MLA John O'Dowd said: "This morning's attack on the M1 has resulted in an utterly pointless death of a prison officer.
"It will resolve nothing either within the prisons or in wider society. It is not part of any strategy or campaign. All it has done is to plunge a family into grief.
"The people responsible, or those who act as their political spokespeople, need to explain themselves to the community."
UUP leader Mike Nesbitt said: "Somebody who got out of bed this morning to do nothing more unusual than to get in his car and go to work has been brutally murdered as he drove along the motorway.
"We're hearing that there's a car burnt out in north Lurgan and so it does seem to have the hallmarks of a terrorist assassination."
SDLP leader Alasdair McDonnell said: "Mr Black's murder marks out the very worst and darkest side of human nature - a side which civilised people banish from their hearts and their societies.
"The slaughter of a man, who left his family in the full expectation of seeing them again that night, is a disgrace to democracy and a true human tragedy.
"The people of Ireland rejected violence long ago and they will continue to reject it today."
Alliance Justice spokesman and East Antrim MLA Stewart Dickson said: "I am absolutely sickened that a prison officer has been targeted in this way.
"There are no words to condemn this brutal attack, which is an attack on our whole society.
"Sadly there are still people focused on keeping Northern Ireland in the past. They must not be allowed to succeed and communities must unite together to show their disgust at this attack."
The people who carried out the attack proved that they could kill a human being - what they can't kill is the peace process.
Church leaders have also united to condemn the murder.
In a joint statement from the Catholic and Church of Ireland Bishops of Dromore, John McAreavey and Harold Miller said: "The tragic and ruthless murder is a morally bankrupt act which has no place in a civilized society. It is to be utterly condemned.
"This is a time for our whole community to come together in declaring that such violence against any person, whatever the motive, is utterly unacceptable."
Presbyterian Moderator Dr Roy Patton added: "Such evil violence contributes nothing to the new society that we are all helping to build and is the complete opposite of the constructive part people like prison officers are taking in building a positive future.
"We know our community will not turn back on the path towards lasting peace and part of that is continuing to give our full and unequivocal support to those who, sadly as today's events show, still put their lives on the line in helping us all on that journey."
Police are urging anyone with information to call 0845 600 8000 and ask for the murder incident room, or to pass information anonymously through Crimestoppers on 0800 555 111.