"Kofi Annan's announcement today that he is no longer available for an extension after his mandate runs out at the end of this month is of course deeply regrettable," Carl Bildt wrote on his blog on Thursday.
Bildt however expressed understanding for the former UN secretary-general Annan's reasons for his decision.
"With a Security Council which is split the possibilities for bringing the various parties in the Syrian conflict together is in reality very slight," he wrote.
Bildt warmly recommended Annan's departing advice on how to save Syria, pointing that that he agreed with his conclusions.
The Swedish foreign minister explained that a divided Security Council allows the opposing parties in a conflict to lean on the support of dissenting groups and resist compromise.
"This is... a universal lesson we have learnt from other similar conflicts and other comparable peace efforts."
While Bildt accepted Annan's assessment that a political solution in Syria currently appears impossible, he argued that efforts should continue.
"It would be fundamentally wrong of the international community to give up its efforts. If a drawn out, bloody, sectarian and regional conflict is to be avoided then some form of political arrangement must be found."
Bildt concluded by saying there were currently few positives in the Syrian situation and expressed a hope that Annan's "tough words" may give international power-brokers new insight "that a political process is necessary".
Peter Vinthagen Simpson