Mr Brown was accompanied by NI Chief Constable Sir Hugh Orde on his visit to the Massereene army base.
One of the two soldiers killed was from the West Midlands, the other was from the London area.
Four other people, including two pizza delivery men, one of whom is Polish, were injured in Saturday’s attack.
The two young soldiers were the first to be murdered in Northern Ireland in 12 years. Lance Bombardier Stephen Restorick was killed by an IRA sniper in 1997.
The dead men, both in their early 20s, were due to fly to Afghanistan in the hours after the attack.
The rest of their regiment has now left the base and gone to Afghanistan.
The dead men’s relatives have been informed of their deaths, but no names are likely to be released today.
Of those who were injured, three are in a serious condition and another is said to be serious but stable in hospital.
The two injured delivery drivers are a 19-year-old local man and a Polish man in his early 30s.
Sinn Fein President Gerry Adams said the murders were “an attack on the peace process”.
“It was wrong. It was counter-productive.
“My thoughts are with the families of the two men who were killed and who were injured,” he said.
“And you might take some succor from the fact that whoever was involved, they have no support and no strategy and no popular will to back up their actions.”
The attack has forced a review of security at police and military bases in Northern Ireland.
Whitehall officials say MI5 has been increasing its resources devoted to counter-terrorism in Northern Ireland.
Police have been examining a car in Randalstown, five miles from the army base, which they suspect may have been used by the gunmen.
The Real IRA was born out of a split in the mainstream Provisional IRA in October 1997.
It carried out Northern Ireland’s worst atrocity when it bombed the County Tyrone town of Omagh, killing 29 people, in August 1998.
The chief constable of the Police Service of Northern Ireland has said he did not believe the attack was a response to him deploying special forces soldiers to gather intelligence on dissident activity.
He added he had no plans to deploy additional military personnel.
“The police deliver policing in Northern Ireland, and that is exactly how it is going to stay,” he said.
Brigadier George Norton, Northern Ireland Garrison Commander, met the Prime Minister and the chief constable at the barracks on Monday.
He said the professionalism of the soldiers of the 38 Engineer Regiment who gave first aid at the scene of the shooting, had helped save lives.
“Our thoughts across the armed services are with the colleagues and friends of these young soldiers who were killed and injured in an horrific attack,” he said.
“Naturally, this has shocked the community and we are all grateful for the sympathies expressed from across Northern Ireland.”
The partner of one of the injured men, who is Polish, and his 16-month-old son live in Antrim. Other members of his family are expected to fly into Northern Ireland today.
Jerome Mullan, the honorary Polish consul in Northern Ireland, said: “He was just here earning a living and now he finds himself caught up in this shocking, disgraceful business.”
Northern Ireland’s First Minister and Democratic Unionist Party leader Peter Robinson offered his sympathies to the families of the victims, and said he and the Deputy First Minister Martin McGuinness would postpone a scheduled trip to the United States.
Mr Robinson said the attack was a “terrible reminder of the events of the past”.
He said information that those responsible had “deliberately turned their weapons on civilians” after murdering the soldiers gave an “idea of the crazed gunmen involved in this”.
“It is the duty of everyone to ensure these people are defeated,” he said.
BBCNEWS, 9 March 2009