"As long as there is British involvement in Ireland, these attacks will continue," Continuity IRA said.
The fatal shooting on Monday night came just hours after Gordon Brown, the British prime minister, said that the two soldiers' deaths would not derail the peace process in Northern Ireland.
Carroll, 48, was shot in the back of the head after responding to a call from a woman in distress in Craigavon, an area known to be home to nationalist republican supporters.
Police and politicians have said they fear a return to tit-for-tat violence following the attacks.
Speaking after Monday night's attack, Peter Robinson, first minister in the Northern Ireland Assembly, said he was "sickened at the attempts by terrorists to destabilise Northern Ireland".
"Those responsible for this murderous act will not be allowed to drag our province back to the past,'' he said.
August, 1969: A Catholic civil rights movement escalates into rioting in Londonderry and Belfast. UK troops return to Northern Ireland
March, 1972: Northern Ireland government is suspended and direct rule imposed from London
1974: Irish Republican Army (IRA) launches bombing campaign in Northern Ireland and on the British mainland
April, 1998: Good Friday Agreement is signed, ending twenty-four years of violence in which 3,000 people were killed
March, 2007: Power-sharing government agreed with devolved power from London
July, 2007: UK troops begin withdrawal
Hugh Orde, Northern Ireland's police chief, said the latest attack appeared to be a "a deliberate set-up".
Dolores Kelly, a member of Northern Ireland's joint Catholic-Protestant policing board, and a member of the nationalist SDLP party, has called for restraint.
"We are tonight staring into the abyss and I would appeal to people to pull back," Kelly said.
Eamon Malley, a journalist and author based in Belfast, told Al Jazeera that questions will rise over the expert nature of the attacks.
"These [dissident groups] are people who have habitually bungled every operation in which they've been involved," he said.
"Now, these are two very ruthlessly efficient operations, carried out with considerable skill and cunning.
"Now why now have they acquired this expertise, particularly in one weekend?"
Malley said that while the political process would not be derailed by the attacks, the people responsible for them were holding politicians to ransom.
"The political system is strong, it's going to withstand this," he said.
"But, I have to say, what's happening now is, this small dissident republican group is holding Gordon Brown to ransom, Peter Robinson, the first minister, and deputy first minister Martin McGuiness to ransom ... They can't even leave Northern Ireland.
"If this group continues, or in a staggered way to escalate their campaign, yes, everybody will be a hostage here."
Brown gave an assurance on Monday that the killing of two British soldiers on the weekend would not affect the Northern Ireland peace process.
Leaders from both sides of the political spectrum have condemned the attack and vowed that it would not harm the power-sharing government which came into effect in 2007.
The attackers opened fire on the soldiers on Sunday as they collected pizzas outside their regiment's headquarters in Massereene, outside Belfast.
Cengiz Azimkar, 21 and Mark Quinsey, 23, were the first soldiers to be killed in the past 12 years in the region.
Two of the wounded were pizza delivery men.
Al Jazeera's Alan Fisher said: "The attacks could cause problems for the peace process on a number of levels.
"Obviously no one wants to see anyone threaten the democratic institutions that have been recreated over the last ten years or so."
The Real IRA claimed responsibility for the Massereene shootings in a phone call to an Irish newspaper, using a recognised code word.
The group split from the provisional IRA after a peace accord in 1998 ended 30 years of violence between those who wanted a united Ireland and those who supported British rule over the province.