Doctors Without Borders, which ran the hospital, has called for the Bern-based body to investigate the strike on a hospital in the northern city of Kunduz on October 3, which killed 22 people, including 12 of the medical charity's staff.
Burkhalter told reporters that Switzerland thought using the International Humanitarian Fact-Finding Commission (IHFFC), an independent mechanism created under international law but which has never before been used, was "a good solution".
MSF has condemned the attack as a war crime and insists an independent probe is needed not only to establish the facts of the attack, but also to reaffirm the international laws protecting humanitarian actors in all conflict zones.
Speaking at a Geneva conference aimed to prepare next year's World Humanitarian Summit in Istanbul, UN Deputy Secretary Jan Eliasson decried "a growing lack of respect for international humanitarian law."
More From This Section
"This is something that we need to react to," he told the some 900 delegates at the Geneva conference.
Burkhalter also lamented a growing disregard for the global rules aimed at protecting civilians and aid workers in conflicts, pointing out that last year 155 humanitarian workers were killed in ongoing conflicts.
He stressed the importance of an upcoming international conference hosted by the Red Cross in Geneva in December aimed at seeking ways and mechanisms to ensure compliance with the Geneva Conventions.
"Here you have the most universal of all conventions, and there is no way to ensure they are respected," he said.
"It is not something that will happen by itself. In fact, it is happening less and less," he warned.