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"As Bruce noted, after the establishment of a ceasefire, the parties will be able to move on to negotiations on other aspects of the conflict settlement.
"We have never been closer to a cease-fire than we are now," the State Department spokeswoman said.
However, the specific terms and conditions of a possible truce have not yet been specified.
Earlier it was reported that diplomats from various countries have stepped up efforts to find ways to de-escalate the situation in the region.