After talks with the UN commander in Bosnia, Lt-Gen Sir Michael Rose, Mr Abdic agreed to respect the nationwide truce, in danger of unravelling because of the battle in Bihac.
"After some discussion, [Rose] got an agreement in principle from Mr Abdic to respect the ceasefire," said Edward Joseph, a UN official in Bihac. But the general's talks with Atif Dudakovic, commander of the Bosnian forces in Bihac, were less fruitful, Mr Joseph said. General Rose "asked them to apply the terms of the ceasefire throughout the pocket - they're still considering this".
General Rose has been trying for weeks to visit the Bihac pocket, where 170,000 civilians and 1,200 peace-keepers were trapped for weeks without sufficient food or medicine. But until this week the Krajina Serbs who hold Croatian land around Bihac had refused him permission to enter the enclave. General Dudakovic's troops, who defeated a year-long Abdic rebellion in August and then marched on Bosnian Serb positions, lost ground in a three-pronged counter-attack in November by the two Serb armies and Mr Abdic.
The Bosnian Serb lines around the town of Bihac, a UN "safe area", have been quiet since the ceasefire began on Christmas Eve, but fighting has continued near Velika Kladusa, a town retaken by Abdic and Krajina Serb forces.
Mr Joseph said the government's main concern was with Serb rebels attacking across the border from Croatia. "Their position has been clear all along," he said. "It's not primarily a problem with Mr Abdic but with the Krajina Serbs."
Neither force is party to the truce; Sarajevo argues that both are acting in concert with the Bosnian Serb leadership in Pale and should therefore respect it. If not, Sarajevo says its forces will be compelled to attack elsewhere, to relieve the pressure. There is some UN sympathy for this position, allied to fears that it might offer the government an excuse to break the ceasefire.
"The root of the problem is [the Krajina Serbs] are crossing the border and attacking Bosnia. We know [General Ratko] Mladic has a lot of influence over them, so some of the blame can be traced back to Pale," said one UN official, referring to the Bosnian Serb commander. Another explained: "The fighting in the north of the [Bihac] pocket is principally a Krajina Serb operation."
Yesterday UN monitors detected 89 detonations in the area of Velika Kladusa, but could not identify their origins. Elsewhere in Bosnia, the ceasefire was generally respected.
In Sarajevo, a 61-year-old woman was wounded by sniper fire on Tuesday; yesterday the warring factions traded gunfire across the front line at the Bridge of Brotherhood and Unity near the city centre.
General Rose is also negotiating a cessation of hostilities, due to start on New Year's Day, between Sarajevo and Pale.
Whether Mr Abdic - and, more importantly, the Krajina Serbs - feel the same way remains to be seen.
But the Muslim tycoon is clearly keen to get back to business: during yesterday's meeting he asked the UN to transport 9,000 live chickens to Velika Kladusa so that he could kick-start his agro-industrial empire.