"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.
"We will appoint dedicated officers in the Foreign Office and our Embassy in Tripoli who will accompany the campaign group to meetings with the Libyan government to negotiate compensation, the first of which will be in the next few weeks."
Critics say the government has shied away from confronting the Libyan leader, Colonel Muammar Gaddafi, because of deals struck with Tripoli by British oil companies.
But the prime minister insisted "successive governments" had sought compensation for IRA victims over last two decades.
He said: "Our priority has been to ensure that Libya supports the fight against terrorism and gives up its nuclear weapons.
"As Libya has renounced nuclear weapons and terrorism, our relationship has changed.
"It is these concerns - not oil or commercial interests - that have long been the dominant feature of our relationship."
Mr Parry said the government's main consideration should be the safety of its citizens
Mr McCue said it was "a great day for victims" because Gordon Brown had made a "principled decision" that "listened to ordinary folk rather than bureaucrats".
"I am confident that his moral and logistical backing for the British victims of Libyan Semtex will ensure that they now receive justice and compensation, as did the US victims when they received the support of their president," he said.
Mr McCue added that "with our PM's full support, I cannot see why this matter cannot be concluded swiftly in a matter of weeks and before parliament reconvenes."
Northern Ireland MP Jeffrey Donaldson, who has been working with the victims' families and is due to visit Tripoli on their behalf, said: "We have forced a U-turn, it's not every day you can say that.
"We will work with his government to put the case to the Libyans.
"It is essential now that the government delivers what the Prime Minister has promised."
The government denied claims it refused to press for compensation because of fears of jeopardising oil deals with Libya.
On Sunday Downing Street released a letter written by the prime minister to IRA victims' lawyer Jason McCue last October in which Mr Brown wrote that the government did not "consider it appropriate to enter into a bilateral discussion with Libya on this matter".
Libya are an essential partner in the fight against terrorism and it is in the UK's interests for this co-operation to continue
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