On Sunday, a dissident republican group claimed responsibility for the shootings in a phone call to an Irish newspaper, using a recognised code word.
The Sunday Tribune said it received a telephone call from a purported spokesman of the Real IRA, which says it is fighting to end British rule in the province.
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.
Brown said the perpetrators "have got to be hunted down and brought to justice as quickly as possible".
He said: "The Real IRA have no place in the politics of Northern Ireland.
"These are callous murderers, these are terrorists who showed no sympathy towards people who were dying."
The attackers opened fire on a group of British soldiers as they collected pizzas outside the headquarters of the Royal Engineers in Northern Ireland at Massereene, northwest of the Irish capital.
The British defence ministry named the dead soldiers as Cengiz Azimkar, 21, from London, and Mark Quinsey, 23, from Birmingham.
They are the first soldiers to be killed in the last 12 years in the region.
Two of those wounded were pizza delivery men.
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.
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.
Last week, Hugh Orde, Northern Ireland's police chief, warned of possible attacks by republican fighters.
Northern Ireland witnessed three decades of civil unrest known as "the Troubles" in which around 3,000 people were killed.
Such attacks in Northern Ireland are now relatively rare, but the last 18 months have seen an upsurge in violent activity from republicans opposed to the peace process.