David Cameron has ordered Whitehall officials to launch an investigation into the Muslim Brotherhood – drawing on assessments by MI5 and MI6.

Speaking at a No 10 news conference, the prime minister said that the government was committed to encouraging people away from the path of extremism.

"We want to challenge the extremist narrative that some Islamist organisations have put out," he told reporters following talks with new Italian prime minister Matteo Renzi.

"What I think is important about the Muslim Brotherhood is that we understand what this organisation is, what it stands for, what its beliefs are in terms of the path of extremism and violent extremism, what its connections are with other groups, what its presence is here in the United Kingdom. Our policies should be informed by a complete picture of that knowledge," he said.

"It is an important piece of work because because we will only get our policy right if we fully understand the true nature of the organisation that we are dealing with."

A No 10 source confirmed a report in the Times that the investigation is being launched as the prime minister faces pressure to follow the example of Egypt and Saudi Arabia, which claim that the Muslim Brotherhood uses London as a crucial centre for its activities, to ban the group.

The Times reported that MI6, Britain's overseas intelligence agency, would examine claims that the Muslim Brotherhood was behind the bus attack in Egypt. MI5 will assess how many leaders have been based in Britain after last year's coup in Egypt in which Mohamed Morsi, the Muslim Brotherhood president, was ousted.

The regime of Abdel Fattah el-Sisi, the head of the Egyptian armed forces who played a leading role in the overthrow of Morsi last year, has placed the former president on jail where he awaits trial for treason. Morsi was the candidate for the Muslim Brotherhood's Freedom and Justice party for the 2012 presidential elections in Egypt.

Cameron ordered the investigation after it was concluded that Whitehall has insufficient intelligence about the Muslim Brotherhood's activities in Britain and in Egypt. Downing Street has asked Sir John Jenkins, the British ambassador to Saudi Arabia to draw up a report on the Muslim Brotherhood's "philosophy and values and alleged connections with extremism and violence".

Sir Kim Darroch, the prime minister's national security adviser, has already started work. A key role will be played by Sir John Sawers, the current chief of the Secret Intelligence Service (MI6), who served as UK ambassador to Egypt between 2001-03. Sawers, who had previously served as Tony Blair's foreign affairs adviser in Downing Street, had strong contacts with the regime of the former president Hosni Mubarak.

The Muslim Brotherhood, which was founded in Egypt in 1928, was branded a terrorist group by the Egyptian authorities last year. It had been banned during most of the latter part of the 20th century up until the Arab spring which saw the overthrow of Hosni Mubarak as Egyptian president.

British officials are saying it is "possible but unlikely" that the Muslim Brotherhood will be banned in Britain on the grounds of terrorist links. Foreign Office officials figures have until now resisted proscribing the organisation on the grounds that that could encourage extremists. "The truth is that this is a large, disparate organisation that takes different forms in different countries," an official told the paper.

The security services are said to take a more hardline view. Sir Richard Dearlove, the former head of MI6, has reportedly described the Muslim Brotherhood as "at heart a terrorist organisation".

A Downing Street spokesman told the Times: "The Muslim Brotherhood has risen in prominence in recent years but our understanding of the organisation, its philosophy and values, has not kept pace with this. Given the concerns about the group and its alleged links to violent extremism, it's absolutely right and prudent that we get a better handle of what the Brotherhood stands for, how they intend to achieve their aims and what that means for Britain."