David Cameron and Barack Obama have said they are determined to "confront" militant group Islamic State (IS).
Writing in the Times ahead of a Nato summit in Wales, the UK and US leaders said people who wanted an "isolationist approach" misunderstood the situation.
They also said Nato must have a strong presence in eastern Europe to warn Russia against interfering in Ukraine.
Meanwhile, two senior UK figures have called for talks with Syria's President Assad to reinforce efforts against IS.
The US is using air strikes against the group but so far Britain has not done so.
"Developments in other parts of the world, particularly in Iraq and Syria, threaten our security at home," they said.
They also said the UK and US would "not waver in our determination to confront" IS, adding: "Countries like Britain and America will not be cowed by barbaric killers."
After a meeting of the government's Cobra emergency committee on Wednesday, Foreign Secretary Philip Hammond said air strikes had not been ruled out - but the government said there had been no change of strategy towards dealing with IS.
Hammond also said "every possible option" would be considered to protect a UK hostage being held by IS.
An IS militant threatened to kill the Briton during a video showing the killing of US journalist Steven Sotloff, the second such video released in recent weeks.
Later, former Defence Secretary Liam Fox called on the prime minister to support military action.
"I detect a hardening of attitude among MPs who, with every atrocity, want to know why we're not using every means at our disposal to deal with the threat," he added.
'TALK TO ASSAD'
A year ago, British MPs narrowly voted not to take military action against the regime of Syrian President Bashar al-Assad, which was accused of using chemical weapons against its own people during the country's ongoing civil war.
But the regime opposes IS, leading to calls for talks with Assad.
William Patey, a former British ambassador to Iraq and Saudi Arabia, told BBC Newsnight Britain "shouldn't rule out" a deal that "brings together the Assad regime and the known IS opposition together with Iran, with Russia, with the Saudis".
Labour MP Peter Hain, former Northern Ireland and Welsh secretary, said the West could not "resolve the Syrian side of the conflict" with IS unless it dealt with Assad.
Former International Development Secretary Andrew Mitchell said Britain should try to "galvanise the United Nations into taking action".
"This is not a problem that is going to be resolved by action just by America and Britain and it's certainly not a problem that's going to be resolved by smart weapons being delivered from 12,000 feet," he said.
In their Times article, Cameron and Obama said Nato must stand up to Russia, which has been widely accused of sending troops into Ukraine.
"With Russia trying to force a sovereign state to abandon its right to democracy at the barrel of a gun, we should support Ukraine's right to determine its own democratic future and continue our efforts to enhance Ukrainian capabilities," they wrote.
"We must use our military to ensure a persistent presence in eastern Europe, making clear to Russia that we will always uphold our... commitments to collective self-defence.
"And we must back this up with a multi-national rapid response force, composed of land, air, maritime and special forces, that could deploy anywhere in the world at very short notice."