The request came in a letter from the Yemeni President, Ali Abdullah Saleh to Tony Blair, handed to Victor Henderson, the British ambassador in Sanaa.
According to the official news agency, it "included a request by the Yemeni government to hand over the terrorist Abu Hamza al-Masri, who is residing in London, to be tried on charges of carrying out terrorist activities in Yemen and in several other Arab states."
A spokesman for the Home Office said it neither confirmed nor denied extradition requests as a matter of course.
Earlier a senior Yemeni official expressed his anger over Britain's behaviour to Yemen since the killing of the hostages on 28 December. "Yemen is being subjected to a stream of smears in the mass media instigated by the Foreign Office," he said.
He was particularly enraged by the lack of British government action against Abu Hamza, the head of the Supporters of Sharia (Islamic law) group based in Finsbury Park, north London, who says he isan Afghan war veteran who lost his hands in a mine explosion. The sheikh had just said on the Arab satellite television channel al-Jezira, widely watched in Yemen, that foreign visitors to the country were "like dumb animals; whoever imprisons them can do what he likes with them". He said Yemen was not a Muslim state because it was not based on the Sharia. By his own account Abu Hamza had told the kidnappers to "do all you can to preserve the blood of Muslims", implying that it was acceptable to kill Christians.
The exact relationship between Abu Hamza, with his calls for holy war, the five British Muslims on trial this week in Aden for planning armed attacks and Abu Hassan, the leader of the kidnap gang who killed the four tourists, is still unclear. But to the Yemeni government it looks like a plot instigated from Britain with the knowledge of British intelligence.
"Abu Hamza did not hide his intelligence connections," said the Yemeni official. "Soon you will not be able to tell the difference between London and Tehran [as centres for Islamic militants]."
He pointed to the telephone conversation, made at the time of the kidnapping, between Abu Hamza in London and Abu Hassan in his mountain hideout, as evidence of Abu Hamza's role in the hostage-taking. He added that the involvement of the British group facing trial in Aden was underlined by the fact that one of them, Mohsin Ghalain, is Abu Hamza's step-son and his full son, Mohammed Mustapha Kamil, is on the run in Yemen.
Abu Hamza said last night he was not worried by the extradition request. "The Yemenis have a big cheek to ask for my extradition here", he said.
"Their economic policy in Yemen has forced the Yemeni people to resort to kidnapping to get their basic rights, so the situation is of their own making." He said it was "hypocritical to say the least to allow Salman Rushdie to publish what he calls a dream but then persecute [the group] Supporters of Sharia for simply reporting true events abroad.