Al-Qaeda in the Arabian Peninsula's claim that it was behind the attack has also focused attention on the threat from Yemen.
Abubakr al-Qirbi, Yemen's foreign minister, said this week there could be up to 300 al-Qaeda fighters in his country, some of whom may be planning attacks on Western targets.
Al-Qirbi appealed for more help from other countries to combat the threat.
Brown's office said the London meeting would seek to encourage and co-ordinate efforts by international donors to foster development in areas of Yemen most at risk of radicalisation.
It would discuss what the Yemen government needed to combat extremism and seek international pledges to train Yemeni security forces, it said.
The meeting would also aim to improve co-ordination of international counter-terrorism efforts in the region and to promote economic, social and political reform in Yemen.
'Enemies of democracy'
The prime minister's office said the summit would be held in parallel with the previously announced conference on combating the Taliban in Afghanistan because the issues were inter-related and because key delegates would take part in both events.
Foreign ministers, including Hillary Clinton, the US secretary of state, and some heads of government are expected to attend the Afghanistan meeting.
|Clinton is expected to attend the conference in London [GALLO/GETTY]
In his statement on Friday, Brown said: "Enemies of democracy and freedom, now trying to mastermind death and destruction from Yemen as well as other better-known homes of international terror such as Pakistan and Afghanistan, are concealing explosives in ways which are more difficult to detect."
"Al-Qaeda and their associates continue in their ambition to indoctrinate thousands of young people around the world with a deadly desire to kill and maim.
"Our response in security, intelligence, policing and military action, is not just an act of choice but an act of necessity."
US officials said this week that Washington was looking at ways to expand military and intelligence co-operation with the government of Yemen to increase pressure on al-Qaeda fighters.
Abdulmutallab studied engineering at University College London from 2005 to 2008 and the failed attack has turned a spotlight on Britain's record in countering Islamic extremisim.
The New York Times said this week that, if Abdulmutallab was radicalised in Britain, it would show that Britain, a close US ally, "poses a major threat to American security".
Brown's office said the plan for the Yemen meeting had received strong support from the White House and the European Union.
"In the coming days, Britain also aims to secure backing from Saudi Arabia and Gulf countries," it said.
The UK had ordered a review of airport security arrangements, with Brown promising action "as quickly as possible".
This could include the use of full body scanners at airports, only previously used to a limited extent.