Even before his plane had received clearance for the flight to Belgrade - almost a full day later than planned - the US stated categorically that it would not agree a ceasefire in return for their release and said there could be no preconditions.
Mr Kyprianou's arrival in Belgrade was accompanied by leaks from sources "close to the Yugoslav President", Slobodan Milosevic, that even if he agreed to meet Mr Kyprianou, which was by no means guaranteed, "there will not be any release of the soldiers".
Mr Kyprianou decided to remain in Belgrade overnight in the hope of meeting Mr Milosevic today. A senior Greek government official was quoted as saying: "The latest is that Mr Kyprianou will meet Mr Milosevic on Friday to discuss humanitarian issues that could lead to the release of the three soldiers." But he said that this could change. The servicemen, part of a detachment of 350 US soldiers stationed in Macedonia, had been on a routine patrol on the border with Kosovo when they were taken prisoner.
The Pentagon maintains that they were abducted, but has become increasingly vague about its earlier insistence that they were clearly on the Macedonian side of the border.
The men were shown on Belgrade television shortly after their capture and appeared to have been beaten. Since then there have been no more pictures. The Yugoslav authorities say that they are being well treated, but according to US officials have ignored requests for a visit from a Red Cross representative.
There have been diplomatic contacts over their fate, through Swedish diplomats who are representing US interests in Belgrade.
So far as is known, they are the only Nato troops to be in Yugoslav hands. A US pilot whose F-117 "Stealth" aircraft was shot down on the second night of the Nato strikes was rescued within six hours of ejecting.