The Prime Minister's statement came at the Nato summit near Newport in south Wales yesterday, two days after the British-born killer of US journalists James Foley and Steven Sotloff threatened to kill another hostage, 44-year-old aid worker David Haines, of Perth.
It emerged Tory MPs were being sounded out on the idea of air strikes as Mr Cameron faced growing calls to join America in taking targeted action, he pledged to "use everything we have in our armoury" to squeeze the terror group out of existence.
He said: "I'm not ruling anything out and I will always act in the British national interest."
Later, Mr Cameron dismissed the idea that air strikes in Syria would be illegal without President Assad's approval, saying: "I don't think it's that complicated because obviously the Iraqi government is a legitimate government...whereas President Assad has committed war crimes on his own people and is therefore illegitimate."
Ed Miliband said he "would look at the merits" of any British strike the UK Government put forward. "It's a threat which can't be ignored. It's very, very important that we don't just turn away from it and say 'it's too big a problem'." said the Labour leader.
Reports at Westminster said Conservative MPs were now being sounded out by whips on whether they would back UK involvement in military action against IS.
Deputy Prime Minister Nick Clegg made clear any air strikes "would have to be part of a wider approach which hasn't been assembled yet".
Tory backbencher Rory Stewart, who chairs the Commons Defence Committee, said he had not personally been approached by the whips but noted: "People are obviously reacting to the Syria vote last year, where the Government thought that they were going to be able to do air strikes in Syria but found that Parliament opposed it. They are feeling the water."
Yorkshire-born Mr Haines, who attended Perth Academy, is a father of two who had a military career before working with aid agencies in Syria, Libya, the former Yugoslavia and South Sudan.
He was a consultant director for a manufacturing firm in Croatia and worked with Handicap International on a programme to remove mines in Libya three years ago. He later travelled to South Sudan as a security manager for a peacekeeping force.
The Herald abided by a request of his family and the Foreign Office not to name him in the immediate aftermath of a video from the Islamic State showing Mr Haines, and the threat to kill him. However, his name has subsequently been widely reported in the UK and around the world.
Whitehall sources also signalled the UK Government might be prepared to send arms to the Kurdish forces in northern Iraq, but that this depended on a new Baghdad government being formed that was inclusive and robust. Talks are on-going about training Kurdish forces in Jordan.