"These crimes once again demonstrate the brutality of ISIL, which is responsible for thousands of abuses against the Syrian and Iraqi people," said the 15-nation UN top forum in a statement here Tuesday.
Regarding Kassig, also known as Peter Kassig, "the members of the Security Council noted that his murder is a tragic reminder of the increasing dangers humanitarian personnel face every day in Syria", it said, adding that they "stressed again that ISIL must be defeated and that the intolerance, violence, and hatred it espouses must be stamped out".
The IS distributed a video Sunday showing that it beheaded Kassig, a fifth Western hostage who was an American aid worker and a former Army Ranger.
The group, whose fighters seized vast swathes of territory in northern Iraq since June and announced the establishment of a caliphate in areas under its control in Syria and Iraq, earlier released videos showing the beheading of two American journalists and two British aid workers.
The Security Council members underlined the need to bring the perpetrators of the terror acts to justice and expressed their deep sympathy and condolences to the families of the victims and to the peoples of the United States and Syria, Xinhua cited the statement as saying.
The Security Council members demanded "the immediate, safe and unconditional release of all those who are kept hostage by ISIL, Al-Nusra Front, and all other individuals, groups, undertakings, and entities associated with Al Qaeda", the statement said.
"The members of the Security Council recalled their demand that all parties involved in an armed conflict comply fully with the obligations applicable to them under international humanitarian law, including to respect and protect all humanitarian personnel," said the statement.
"The members of the Security Council also recalled their condemnation of all forms of violence and intimidation to which those participating in humanitarian operations are increasingly exposed."
They emphasised that such continued acts of barbarism perpetrated by the IS "do not intimidate them, but rather stiffen their resolve that there has to be a common effort among governments and institutions, including those in the region most affected, to counter ISIL, Al-Nusra Front and all other individuals, groups, undertakings and entities associated with Al Qaeda".