In an urgent statement to MPs, Northern Ireland Secretary Theresa Villiers sent her "deepest condolences" to David Black's widow Yvonne, son Kyle and daughter Kyra for their "devastating loss" and vowed to catch his killers.
"The Government will do whatever we can to help the PSNI bring the perpetrators of this atrocity to justice," she said. "We will continue to do everything in our power to ensure the terrorists do not succeed."
Mrs Villiers said yesterday's killing showed the threat posed by dissident republicans.
"The numbers involved in terrorism activities are small, but these groupings have the capability and they have lethal intent," she said. "They can still ruin lives despite their lack of support in the community, so we remain vigilant."
Three men, aged 31, 29 and 44, have been arrested following the killing of prison officer David Black in Northern Ireland.
Leaders in Northern Ireland have condemned the "horrific" motorway murder of a veteran prison officer by suspected dissident republicans.