Cameron will chair a meeting of the government's emergency response committee, Cobra, on Sunday which will be attended by senior representatives of the military and security services, a spokeswoman said.
The prime minister described the beheading of 44-year-old David Haines as "pure evil", after the video was released late on Saturday showing his apparent execution by the Islamic State group, which has swept across Iraq and Syria in recent months.
Cameron said Britain would do "everything in our power to hunt down these murderers and ensure they face justice, however long it takes". It was the third apparent beheading of a Western hostage in less than a month and an Islamic State member seen apparently killing Haines in the video threatened to execute a fourth, another Briton.
The video blamed Cameron for joining forces with the United States, which has said it is at "war" with the group and is currently hitting it with air strikes in Iraq. The government in London faces accusations of confusion over its policy towards the Islamic State after conflicting comments from Downing Street and the Foreign Office last week.
During a visit to Berlin, Foreign Secretary Philip Hammond said Britain would not take part in strikes against IS in Syria, after parliament last year voted against taking military action in that country. But just hours later, a spokesman for Cameron's Downing Street office insisted the prime minister was not ruling anything out.
'Degrade and destroy'
In a statement issued on Saturday night, US President Barrack Obama said the hearts of Americans go out to Haines' family and the people of the United Kingdom.
"The United States stands shoulder to shoulder tonight with our close friend and ally in grief and resolve," Obama said. "We will work with the United Kingdom and a broad coalition of nations from the region and around the world to bring the perpetrators of this outrageous act to justice, and to degrade and destroy this threat to the people of our countries, the region and the world," he said.
In his statement, Obama repeated the pledge he made on Wednesday night in a nationally televised address in which he laid out a strategy to respond to the threat from IS, which is also referred to as ISIL.