Cameron speaks to US and Yemeni leaders after air alert
The prime minister has spoken of his conversations with US and Yemeni leaders after an explosive device was found on a US-bound plane in Britain.
David Cameron said he told President Barack Obama that "we'll go on working closely together" to defeat terrorism.
He had told President Saleh of Yemen that more must be done to "cut out the cancer" of al-Qaeda in his country.
Earlier Home Secretary Theresa May said the UK's terror threat level would stay at "severe".
Mr Cameron said he had told President Saleh "We have to do even more to crack down and cut out the cancer of al-Qaeda in Yemen and the Arabian Peninsula."
He added: "These terrorists think that our connectedness, our openness as modern countries, is what makes us weak - they're wrong; it's a source of our strength."
Of the device itself he said: "We believe that the device was designed to go off on the aeroplane; we cannot be sure about the timing when that was meant to take place.
"There is no early evidence it was designed to take place over British soil but, of course, we cannot rule that out."
The device - a printer cartridge with wires protruding - was on a Chicago-bound plane at East Midlands Airport.
Mrs May said there was no indication another attack was imminent but that unaccompanied air freight from Yemen was being banned from the UK.
Another device was found in Dubai.
Yemeni police are reportedly examining 26 other suspect parcels. Intelligence agencies believe the packages are linked to terrorist group al-Qaeda in the Arabian Peninsula, which is based in the country.
The Yemeni embassy in London said no planes from delivery firm UPS land or take off from the country. Authorities have closed down the offices of UPS and Fedex in the state, the BBC understands.
Speaking after a meeting of government emergency planning committee Cobra, Mrs May said officials were continuing to work with international colleagues on the investigation.
"I can confirm that the device was viable and could have exploded. The target may have been an aircraft and had it detonated the aircraft could have been brought down," she said.
Severe is the second-highest level of alert, meaning an attack is "highly likely". The highest level - critical - indicates an attack is imminent.
Direct flights from Yemen to the UK were suspended in January 2010. Mrs May confirmed that an additional bar had been imposed on all unaccompanied air freight originating from Yemen from coming into or through the UK.
The flight found to be carrying the device at East Midlands Airport had stopped to refuel.
Yemen is considered a source of a growing threat of extremist violence and the UK has been working with the US to strengthen counter-terrorism there.
President Obama praised the professionalism of British officers in a call to the prime minister, the White House said.
Likewise, shadow home secretary Ed Balls said: "This clearly constituted a potentially serious threat to our security and we should all pay tribute to our police and intelligence and security services who, working with international colleagues, located and secured the device."
A Metropolitan Police spokesman said the Met's counter terrorism officers were liaising with international agencies and tests on the device were continuing.
Mr Obama's top counter-terrorism adviser John Brennan said the US was "remaining vigilant".
The packages were destined for Jewish places of worship in Chicago, Mr Obama said.
The alerts were:
- Suspect package found at Dubai
- Suspect package found at East Midlands Airport
- Three cargo planes owned by the freight company UPS searched in Newark and Philadelphia
- US fighter jets escorted Emirates flight 201, which was carrying cargo from Yemen, from Dubai into New York
- Suspect package from Yemen examined on a delivery lorry in New York
- BA flight from London to New York met by authorities amid reports of search of its cargo
Mr Obama stressed that new aviation security measures were being taken in the US, "including additional screening".
US officials told Associated Press they believed the packages contained PETN (pentaerythritol tetranitrate) - the explosive used in the failed bombing of a US-bound airliner last Christmas Day - although full testing was not complete.
BBC security correspondent Gordon Corera said the devices appeared to signal "growing creativeness allied to ongoing ambition" on the part of Al-Qaeda in the Arabian Peninsula.
"Attacking cargo planes has also long been anticipated as a potential tactic. Militant groups regularly look for any weak spots in security, and aviation remains a prime target," he said.
The discovery of the devices may have a similar effect on changing the way cargo is transported as the 2006 "liquid bomb plot" on passenger travel, with new restrictions put into place, he added.