Terrorists should not be allowed to hide behind asylum and refugee laws, the UK foreign secretary told the UN.
Mr Straw said he was proud Britain offered refugees a safe haven
Laws offering protection from abuse by foreign governments need updating in an era of global terrorism, Jack Straw told the UN General Assembly.
"We cannot let terrorists exploit a protection designed for the persecuted, not the persecutors," he argued.
He said Britain and Russia were working on a new Security Council Resolution to stop terrorists evading justice.
The resolution is aimed at stopping those who commit, support or finance terrorist acts from "sheltering behind a refugee status", he told the assembly in New York.
And it would look at allowing terrorists to be extradited more quickly.
Mr Straw said he was proud Britain was part of the 1951 Convention on Refugees and offered the persecuted a safe haven.
And he said no country in the EU would allow suspects to be returned to countries to face the death penalty.
But he continued: "As the 1951 Convention itself sets out, asylum is not an unqualified right.
"It does not apply to anyone who has committed a war crime, a crime against humanity, or other serious crime, or who is guilty of acts contrary to the purposes and principles of the United Nations."
Tory homeland security spokesman Patrick Mercer said his party supported measures to "stop terrorists hiding behind asylum laws".
"But while the government talks tough, Britain is still not adequately protected," he said.
Mr Mercer repeated Conservative calls for the creation of a new Cabinet-level post for homeland security which he argued would "help coordinate Britain's defence against terrorists".
"The organisation of our homeland security at the moment is incoherent," he added.
The foreign secretary also used his speech to call for more discussion of the criteria by which the "international community" should send in troops when people are being abused by their own regimes - citing the examples of Rwanda and Bosnia.
And he asked for unity in defeating the "terrorist insurgency" in Iraq and called on all states to adopt the Kyoto protocol, an international agreement aimed at reducing greenhouse gas emissions.
Russia, meanwhile, has called for the extradition of Chechen political leaders living abroad in the wake of the Beslan school siege.
That includes Akhmed Zakayev, a spokesman for the Chechen rebel leader who is currently in London.
The British government say before they take any action they need evidence of what he is accused of.