The two leaders talked of a "strong partnership"
Gordon Brown has held one-to-one talks with Libyan leader Muammar Gaddafi for the first time, discussing a range of political and economic issues.
The two met for 45 minutes on the sidelines of the G8 summit in Italy.
Issues discussed included the condition of the man convicted of the Lockerbie bombing and the unsolved murder of PC Yvonne Fletcher in London in 1984.
No 10 said the two stressed how much progress had been made recently in relations between the two countries.
Libya's announcement in 2003 that it had abandoned plans for a nuclear weapon resulted in a dramatic improvement in relations with the international community and led to then prime minister Tony Blair's historic visit to Libya a year later.
At Friday's meeting, Mr Brown praised Libya's "brave decision" and said it hoped it would set an example to other countries in efforts to stop nuclear proliferation.
The Libyan leader asked Mr Brown for help in allowing Abdel Basset al-Megrahi, who is serving a life sentence in Scotland for the Lockerbie bombing, to serve the rest of his sentence in Libya.
Tripoli is concerned that al-Megrahi, who is suffering from terminal cancer, may die before the outcome of his appeal against the conviction is known next year.
No 10 said the prime minister had made it clear this was a matter for the Scottish government and not for him.
Mr Brown raised the case of WPC Yvonne Fletcher, who was shot outside the Libyan Embassy while policing a protest and whose killers have not been brought to justice.
The Libyan government has been assisting British detectives investigating Ms Fletcher's murder.
Other issues discussed included the need to reduce oil price volatility and a greater voice for Africa in international bodies such as the World Bank.
The BBC's Chief Political Correspondent James Landale said the prime minister's spokesman had described the meeting as "good and businesslike".
He added that the two leaders had spoken of a "very strong partnership" between their respective nations.