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The situation in Northern Ireland, military strategy in Afghanistan, Iran's nuclear program and climate change also dominated their agenda.
The pair reportedly also discussed the current situation in Pakistan and India.
Clinton's visit came at a time when bilateral ties got in sour due to U.S. irritation over the release of the Lockerbie bomber. Brown had reportedly been snubbed by the White House after requesting a private meeting with U.S. President Barack Obama when he traveled to New York and Pittsburgh last month.
On the Northern Ireland peace process, the U.S. secretary of state said it was imperative the Good Friday Agreement was seen all the way to conclusion.
It is reported that the Irish National Liberation Army (INLA) on Sunday afternoon announced an end to its violence in Northern Ireland.
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U.S. Secretary of State Hillary Clinton speaks during her meeting with Britain's Foreign Secretary David Miliband in London October 11, 2009 |
A representative of the Irish Republican Socialist Party (IRSP) said: "The objective of a 32-county socialist republic will be best achieved exclusively through political, peaceful means."
The U.S. diplomat later flew to Dublin for talks with Irish Prime Minister Brian Cowen on Sunday. They will discuss a range of international issues, as well as the close relationship between Ireland and the United States.