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After a 30-minute meeting at Brown's Downing Street offices, the British leader said Christofias had been instrumental in efforts to reunify the divided Mediterranean island.
"He has shown vision and political courage, reaching out to the Turkish Cypriot community and its leader, inspiring hope in Cyprus both sides of the green line," Brown told reporters.
Brown reaffirmed British support for reconciliation and a "joint and lasting settlement which has evaded us for too long", saying it is right to seek a solution by Greek Cypriots, for Greek Cypriots."
Christofias said that he wants Britain to play a "strong and supportive" role in the United Nations-backed process, Brown added.
Greek Cypriots have often criticized their former colonial ruler for showing bias to Turkey when it comes to solving the island's three-decade-old division. The presence of 10,000 British troops and dependents there is also sensitive.
Relations plunged to a new low in 2006, when Christofias's predecessor, Tassos Papadopoulos, refused to meet Britain's then-foreign secretary Jack Straw after he insisted on meeting the Turkish Cypriot leader Mehmet Ali Talat.
Straw -- now justice secretary and a close ally of Brown -- also faced protests telling him to "go home".
An attempt to mend fences collapsed in October last year when Greek Cypriots objected to a deal signed by London with Ankara that envisaged high-level contacts with the Turkish Cypriots.
Christofias himself once described Britain as Greek Cypriots' "bad demon" due to a popular perception that London works against the interests of Greek Cypriots.
But he said talks with Brown Thursday were "friendly" and emphasized the two nations "common interests" -- the sizeable Greek Cypriot ex-pat community in Britain and other links such as tourism -- and their "close ties".
They also signed a memorandum of understanding to ensure the development of what Brown said was a "strong, forward-looking and meaningful relationship".
Britain's Europe minister, Jim Murphy, is to visit the island in the coming weeks, he added.
"I am committed and I promised the people of Greek Cypriots that I will do my utmost in order to make the relationship between our two countries better, closer and more developed," Christofias said at a brief joint news conference.
Thursday's talks were a chance to build on a previous meeting in Brussels and to "make our co-operation more concrete", he said, adding that he hoped for more regular, even daily, exchanges.
Christofias said the talks touched on Turkey's accession to the European Union, which Britain strongly supports. He reaffirmed Greek Cypriots' backing also, subject to conditions concerning Turkish Cypriots.