The chorus of official applause from international leaders over the death of Osama bin Laden has failed to silence doubts about the killing's legality.

Despite widespread backing for the raid, there is a growing demand for the precise legal basis of the US operation to be explained, particularly given the absence of prior debate in the UN security council.

Prof Nick Grief, an international lawyer at Kent University, said the attack had the appearance of an "extrajudicial killing without due process of the law".

Cautioning that not all the circumstances were known, he added: "It may not have been possible to take him alive ... but no one should be outside the protection of the law." Even after the end of the second world war, Nazi war criminals had been given a "fair trial".

The prominent defence lawyer Michael Mansfield QC expressed similar doubts about whether sufficient efforts had been made to capture Bin Laden. "The serious risk is that in the absence of an authoritative narrative of events played out in Abbottabad, vengeance will become synonymised with justice, and that revenge will supplant 'due process'.

"Assuming the mission was … intended to detain and not to assassinate, it is therefore imperative that a properly documented and verifiable narrative of exactly what happened is made public. Whatever feelings of elation and relief may dominate the airwaves," he said, "they must not be allowed to submerge core questions about the legality of the exercise, nor to permit vengeance or summary execution to become substitutes for justice."

The human rights lawyer Geoffrey Robertson QC argued that the killing risked undermining the rule of law. "The security council could have set up an ad hoc tribunal in The Hague, with international judges (including Muslim jurists), to provide a fair trial and a reasoned verdict," he wrote in the Independent. "This would have been the best way of demystifying this man, debunking his cause and de-brainwashing his followers."

The immediate justification for the killing was that the head of al-Qaida had long ago declared war on the US and other nations. "In war you are allowed to attack your enemy," a US embassy spokesman in London said.

Hillary Clinton, the US secretary of state, echoed Barack Obama's assertion, stating: "Osama bin Laden is dead and justice has been done."

A more thorough explanation of the legal basis was given last year by Harold Hongju Koh, legal adviser at the US state department. He told a meeting of the American Society of International Law: "Some have argued that the use of lethal force against specific individuals fails to provide adequate process and thus constitutes unlawful extrajudicial killing. But a state that is engaged in an armed conflict or in legitimate self-defence is not required to provide targets with legal process before the state may use lethal force.

"The principles of distinction and proportionality that the US applies are …implemented rigorously throughout the planning and execution of lethal operations to ensure that such operations are conducted in accordance with all applicable law."

He added: "Some have argued that our targeting practices violate domestic law, in particular, the longstanding domestic ban on assassinations. But under domestic law, the use of lawful weapons systems - consistent with the applicable laws of war - for precision targeting of specific high-level belligerent leaders when acting in self-defence or during an armed conflict is not unlawful, and hence does not constitute 'assassination'."

John Bellinger III, who served as the state department's senior lawyer during George Bush's second term as president, also insisted the strike was legitimate.

"The killing is not prohibited by the long-standing assassination prohibition in executive order 12333 [signed in 1981] because the action was a military action in the ongoing US armed conflict with al-Qaida and it is not prohibited to kill specific leaders of an opposing force," he wrote.

"The assassination prohibition also does not apply to killings in self-defence. The executive branch will also argue that the action was permissible under international law both as a permissible use of force in the US armed conflict with al-Qaida and as a legitimate action in self-defence, given that Bin Laden was clearly planning additional attacks."

Many human rights groups have reacted with caution. "Osama bin Laden took credit for and supported acts around the world which amounted to crimes against humanity," said Claudio Cordone, senior director at Amnesty International.

"He also inspired others to commit grave human rights abuses. His death will put an end to his role in organising or inspiring such criminal acts. We do not know the full circumstances of his killing and the others with him and we are looking into that." Amnesty is writing to the US and Pakistani governments for "greater clarification about the events that led to the death of Osama bin Laden".

One area of anxiety is the suggestion that the intelligence needed to locate Bin Laden's refuge might have been obtained through torture of suspects detained at Guantánamo Bay or other secret holding centres.

Whether or not the Pakistan government authorised the assault on its territory might technically affect the legality of the operation under international law. But the enthusiastic support of the UN secretary general, Ban Ki-moon, for the killing is likely to silence any critical voices in the security council.

"The death of Osama bin Laden … is a watershed moment in our common global fight against terrorism," Ban said. "Personally, I am very much relieved by the news that justice has been done."