He said Britain had to confront and “ultimately destroy” the “menace” of IS in a “calm, deliberate” way.
“They are not Muslims, they are monsters”, he said.
Mr Haines was seized in Syria in 2013 and appeared at the end of a video showing the beheading of US journalist Steven Sotloff earlier this month.
He was being held by Islamic State militants who had already killed two US captives, and a video of his death came shortly after his family appealed to his captors to make contact with them.
Born in Holderness, East Yorkshire, Mr Haines went to school in Perth and had been living in Croatia with his second wife, who is Croatian, and their four-year-old daughter. His parents live in Ayr.
A video of the 44-year-old’s beheading was released on Saturday night. A masked man who appears to have a British accent was pictured beside Mr Haines holding a knife.
The footage also includes a threat by IS, also known as ISIL and ISIS, to kill a second British hostage.
Speaking after a meeting of the UK emergency committee Cobra, Mr Cameron said: “We will do everything in our power to hunt down these murderers and ensure they face justice, however long it takes.”
He also said the country was “sickened” that a Briton could have carried out the “despicable” killing.
“We cannot just walk on by if we are to keep this country safe,” he said.
“Step by step, we must drive back, dismantle and ultimately destroy Isil and what it stands for.
“We will not do so on our own, but with working with our allies, not just in the United States and in Europe, but also in the region.”
He said the organisation posed a “massive threat” to the entire Middle East and said it would be defeated through a “comprehensive and sustained counter-terrorism strategy”.
He added: “This is not about British combat troops on the ground. It is about working with others to extinguish this terrorist threat.”