Two of those wounded were pizza delivery men.
Breen said the Real IRA spokesman decribed the pizza delivery men as "collaborators with British rule".
Jonathan Moore, a Northern Ireland expert at London Metropolitan University, told Al Jazeera that the Real IRA, which carried out a bombing in the town of Omagh in 1998 killing 29 people, were the most likely group to have carried out the attack.
August, 1969: A Catholic civil rights movement escalates into rioting in Derry and Belfast. UK troops return to N Ireland.
March, 1972: N Ireland government is suspended and direct rule imposed from London.
1974: Irish Republican Army (IRA) launches bombing campaign in 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.
"There are a great number of small dissident republican groups in Northern Ireland, the Real IRA are the most significant," he said.
"Since the mainstream provisional IRA gave up its arms, all kinds of small groups, many of them very locally based, have come into existence and we have had splits and further splits which mean that any kind of control becomes more difficult."
The Real IRA 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.
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 to power in 2007.
"Their intention is to bring British soldiers back onto the streets. They want to destroy the progress of recent times and to plunge Ireland back into conflict," Gerry Adams, president of the Sinn Fein party which led opposition to British rule, said.
"Our responsibility is to defend the peace process and the progress that has been made to achieving national and democratic rights," he said in a statement.
Peter Robinson, the first minister in the Northern Ireland Assembly, urged pro-British unionists not to retaliate against the Catholic community.
"Can I urge all of those who may be angry within the unionist community ... this is a matter to be left entirely with the police and the authorities," he said.
Gordon Brown, the British prime minister, said that the killings would not stop the peace process in the province from moving forward.
"I can assure you that we will bring these people to justice," he said.
"No murderer will be able to derail a peace process that has the support of the vast majority of the people of Northern Ireland and we will step up our efforts to make the peace process one that lasts and endures."
Brian Cowen, the Irish prime minister, also condemned the attack, saying: "A tiny group of evil people cannot and will not undermine the will of the people ... to live in peace together."
Derek Williamson, the police chief superintendent who is leading the hunt for the attackers, said that the six victims were believed to have been wounded during the initial volley of bullets before some were shot again at close range.
The attackers' vehicle was later found in the nearby town of Randalstown.
Shane Greer, a Northern Ireland political analyst, described the attack as a criminal act.
"The last time a British soldier was murdered in Northern Ireland by terrorist forces was 1997," he told Al Jazeera.
"We shouldn't elevate this beyond what it is. It is an act of criminal barbarism. These people will in no way derail the peace process in Northern Ireland."
Last week, Hugh Orde, Northern Ireland's police chief, warned of possible attacks by republican paramilitaries.
Northern Ireland endured three decades of civil unrest known as the Troubles in which around 3,000 people were killed.
Paramilitary attacks in Northern Ireland are now relatively rare but the last 18 months have seen an upsurge in violent activity from republican paramilitaries opposed to the peace process.