David Cameron has said more could be done to speed up the UK's extradition process, after Abu Hamza al-Masri was found guilty of supporting terrorism.

The prime minister said while it took 10 years to remove the radical Muslim cleric from the UK, justice was done.

Abu Hamza could face a life term when sentenced in September. He is to appeal his conviction by a New York court.

His trial heard he aided the kidnappers of 16 tourists in Yemen in 1998 and tried to build a terror training camp.

Mr Cameron told BBC Radio 4's Today programme he thought it was "good that he has faced justice", but that the government must "reflect on whether we can extradite faster".

By Dominic Casciani, BBC home affairs correspondent

Why did Abu Hamza's extradition take so long?

Firstly, judges were dealing with an unprecedented situation: multiple extradition requests from the US for a group of men who were accused of terrorism offences while they were based in the UK.

The cases involved unique circumstances and complex questions which, taken together, had never been put before our courts. These included whether controversial conditions in some maximum security American jails were humane.

So it was inevitable that there would be appeals, as our law allows, all the way to Europe: that is what happens in difficult cases.

The courts have now answered those questions - and that means future extraditions will be more speedy.

Secondly, the cleric's extradition was halted because after years of doing nothing, the UK's authorities suddenly decided in 2006 that they wanted to prosecute after all. The US was told to get to the back of the queue and wait until the end of that British trial. So, in all, Abu Hamza's case was as exceptional as you can get.

Abu Hamza was extradited from the UK, where he preached at the Finsbury Park mosque, after having been jailed for seven years for inciting murder and racial hatred.

Mr Cameron said the government would "reflect on" speeding up extradition and deportation.

"We also need to look... at the European Convention on Human Rights and the position we have got to get into in which if someone threatens our country, we should be able to deport them if they have no right to be here," he said.

In New York the jury of eight men and four women reached a unanimous guilty verdict on all 11 terror charges.

Manhattan US Attorney Preet Bharara said Abu Hamza "was not just a preacher of faith, but a trainer of terrorists".

Abu Hamza was arrested in May 2004 on a US arrest warrant.

The 11 charges against him, external included allegations that he arranged satellite communications for a group of kidnappers in Yemen who carried out a deadly attack in which four hostages were killed.

He was eventually also found guilty of conspiring in 1999-2000 to establish an al-Qaeda training camp in Bly, Oregon in the north-western US, among other acts.

He was convicted of various crimes including hostage taking, conspiring to provide material support to terrorists, and abetting religious war in Afghanistan.

Abu Hamza's defence team said he would appeal, claiming that too much weight had been given to comments he had made on unrelated matters.

His lawyer, Joshua Dratel, told BBC Radio 4's Today programme that Abu Hamza expressed himself "in a manner that was open, very controversial, very honest, very objectionable in many respects with many people's points of view".

He said those people were entitled to their points of view just as Abu Hamza was to his.

"What that doesn't do is make him a criminal," Mr Dratel added.

"And unfortunately, we think that the tenor of his remarks and the way that they were admitted in this case in sort of trigger points for United States, particularly a New York jury, 9/11, Osama Bin Laden, al-Qaeda, all of that created an atmosphere in which the evidence was not evaluated."

Born Mustafa Kamel Mustafa, Abu Hamza al-Masri came to Britain from Egypt in 1979.

He told the court he lost an eye and both his hands - not, as he had previously claimed, from fighting the Soviets in Afghanistan - but during an accident in Pakistan when liquid explosives intended for use in a road construction project went off by mistake.

It was after this that he began wearing a hook in place of his hands which, along with his missing eye, made him a distinctive figure among British Islamists.

His defence claimed in the trial that he had assisted MI5 "to keep the streets of London safe".

But the prosecution portrayed him as a terrorism boss, recruiting and despatching young men on missions around the world.

They said the calm figure who had appeared during the trial - and who will be sentenced on 9 September - was a fraud.