The statement said it would also resume talks with the de Chastelain decommissioning body when it was satisfied the peace process would be advanced by these discussions.
The discussions form part of the tentative peace process, whose future is uncertain.
Mr Gilmore said there had also been discussions on a new round of European peace funding for Northern Ireland.
The discussions had centred on both the Afghan-led peace process and on strengthening co-operation between Afghanistan and Pakistan, he said.
U.S. officials have said that Syria is free to bring up any issue it wishes at the conference, which will include discussions on a "comprehensive" Arab-Israel peace deal.
And discussions will also cover our combined strategy to bring peace and security to Afghanistan, longer-term bilateral relations, shared responsibility behind efforts to improve accountability and the performance of the Afghan government, and the growth of the Afghan economy in sustainable ways.
Our goal in any of this is to create an atmosphere of trust and open dialogue to bring these two sides together so that the discussions can be substantive in moving towards comprehensive Middle Eastern peace.
It's the groups first official discussions with a major power, which is also a Middle East peace mediator.
In other words, people who had substantive discussions with their doctor about their end-of-life preferences were far more likely to die at peace and in control of their situation, and to spare their family anguish.
The decision comes on the heels of a visit two weeks ago by Middle East envoy George Mitchell to Syria, where he said he had "serious and productive discussions" with Syrian President Bashar al-Assad about President Obama's goal of a "comprehensive peace, " which includes peace between Israel and Syria, and Israel and Lebanon.
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