"I desperately care about what has happened to those people who have been victims of IRA terrorism," Brown said at a press conference in Berlin.
Campaigners say Libya shipped Semtex explosives in the 1980s and 1990s to IRA republican bombers fighting to end British rule of Northern Ireland.
Brown said he would provide "dedicated" Foreign Office staff to assist victims and their lawyers in their fight for compensation.
Diplomats at the British embassy in Tripoli would also accompany and advise the group when they travelled to Libya in coming weeks to seek direct talks with Kadhafi on the issue, he said.
"So I think it is clear that we are taking what action we believe is necessary to support the families in the difficult but necessary attempt to represent themselves with the Libyan authorities."
Brown, whose government is under pressure over its dealings with Libya, made the comments during the conference with Chancellor Angela Merkel in the German capital, where they are holding talks ahead of the G20 summit.
Victims of IRA bombings had earlier Sunday accused Brown of putting commercial deals before justice, after leaked letters showed the prime minister considered pressing Tripoli "inappropriate".
The letters in the Sunday Times newspaper piled pressure on Brown amid a row over the release of the Lockerbie bomber -- the only person convicted of the 1988 plane bombing over the Scottish town of Lockerbie that killed 270 people.
Abdelbaset Ali Mohmet al-Megrahi was freed from prison in August on compassionate grounds by the Scottish government back to Libya, where he received a hero's welcome.
His release was condemned by the United States, where many of the victims had lived, and sparked allegations of links to lucrative trade deals with Libya -- something Britain has strongly denied.
Brown wrote to the IRA victims' lawyer Jason McCue in October 2008 saying it was not "appropriate" to enter into bilateral talks with Libya on the issue of compensation, one of the letters, later released by Downing Street, said.
He said "trade" was not the "core reason" for his decision, adding: "While the UK-Libya relationship does indeed include trade, bilateral co-operation is now wide-ranging on many levels, particularly in the fight against terrorism.
"I believe it is in all our interests for this co-operation to continue."
Brown said Sunday he thought the IRA victims themselves, not the government, stood the best chance of persuading Libya to compensate them.
"The Libyans have refused to accept a treaty or normal intergovernmental agreement on this issue," he said.
"As a result, our judgement has been that the course more likely to bring results is to support the families and their lawyers in their legal representations to the Libyan authorities."
The prime minister stressed that the government's priority in recent years has been to ensure that Libya "supports the fight against terrorism instead of sponsoring terrorism and gives up its nuclear weapons."
In Britain, victims of IRA violence hailed Brown's comments as a major breakthrough.
"We welcome at long last that Gordon Brown has taken the steps that he needed to take, we hope he follows through - we will be holding him to what he has said," said William Frazer, who lost family members and friends.
Northern Ireland lawmaker Jeffrey Donaldson, who is part of the delegation due to travel to Tripoli for talks, said: "We have forced a U-turn, it's not every day you can say that."
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