LONDON (AFP) - British Prime Minister David Cameron said Tuesday he had ordered an investigation into the Muslim Brotherhood over concerns that the group, declared a terrorist organisation by Egypt and Saudi Arabia, is linked to violent extremism.

Key leaders of the group have been based in London since the toppling of the Islamist Egyptian president Mohamed Morsi last year and a crackdown that has seen hundreds killed and thousands arrested.

Egypt welcomed the British inquiry, which will reportedly see intelligence agencies assessing claims that the Brotherhood was linked to a suicide bus bombing that killed three South Korean tourists in February and to other attacks.

Cameron said the inquiry was partly because of concerns over extremism following the brutal murder of British soldier Lee Rigby in a crowded London street by two Islamist converts last year.

"What I think is important about the Muslim Brotherhood is to make sure we fully understand what this organisation is, what it stands for, what its links are, what its beliefs are in terms of both extremism and violent extremism, what its connections are with other groups, what its presence is here in the United Kingdom," Cameron told a joint press conference with visiting Italian premier Matteo Renzi.

The inquiry by Britain's ambassador to Saudi Arabia, John Jenkins, would paint a "complete picture" of the organisation, Cameron added.

Egypt's foreign ministry spokesman Badr Abdelatty welcomed the investigation, saying in a statement that he "hoped the matter will be addressed with the necessary seriousness and attention".

The Brotherhood's leader Gomaa Amin, who came to London before the coup for medical treatment, and Ibrahim Munir, a member of the group's guidance council, are both currently based in the British capital.

The group's press office is also based in the city.

They gathered in a flat above an Islamic charity office in the drab northwest London suburb of Cricklewood, according to the Times newspaper, which first reported details of the investigation.

The Muslim Brotherhood did not immediately respond to a request for comment by AFP.

But a spokesman was quoted by The Times as saying it was a "religious obligation for any Muslim Brotherhood member" to cooperate with the review and to respect British laws.

The Brotherhood was founded in Egypt in 1928 and despite years of repression it remains the largest Islamic movement in the Middle East, having particularly returned to prominence during the Arab Spring.