Prime Minister David Cameron says the device in a package sent from Yemen and found on a US-bound cargo plane was designed to go off on the aircraft.
But Mr Cameron said investigators could not yet be certain about when the device, intercepted at East Midlands Airport, was supposed to explode.
A second device containing explosives was found on a cargo plane in Dubai. The US suspects al-Qaeda involvement.
In Yemen, police have arrested a woman suspected of posting the packages.
She was detained in the capital, Sanaa, after being traced through a telephone number she had left with a cargo company, officials said.
The unnamed young woman, described as a medical student and the daughter of a petroleum engineer, was arrested on the outskirts of the city, a security official told AFP news agency. Her mother was also detained but was not a prime suspect, the arrested woman's lawyer said.
President Ali Abdullah Saleh said the US and the United Arab Emirates had provided Yemen with information that helped identify the woman and pledged that his country would continue fighting al-Qaeda "in co-operation with its partners".
"But we do not want anyone to interfere in Yemeni affairs by hunting down al-Qaeda," he added, as heavily armed troops patrolled Sanaa.
The Yemeni authorities also closed down the local offices of the US cargo firms UPS and FedEx, who had already suspended all shipments out of the country and pledged full co-operation with investigators.
US President Barack Obama's national security adviser, John Brennan, has phoned Mr Saleh to offer US help in fighting al-Qaeda, the White House said.
The US authorities have been impressed by the speed and determination the Yemeni authorities have shown in their response, the BBC's Jon Leyne reports from Cairo.
The explosive devices, which triggered security alerts in the US, UK and Middle East, were apparently both inserted in printer cartridges and placed in packages addressed to synagogues in the Chicago area.
Pentaerythritol tetranitrate (PETN) - an explosive favoured by the Yemeni-based militant group, al-Qaeda in the Arabian Peninsula (AQAP) - was discovered in the device intercepted in Dubai.
Mr Obama discussed the apparent terrorist plot with Mr Cameron by phone on Saturday, expressing his "appreciation for the professionalism of American and British services involved" in disrupting it, the White House said.
Later, Mr Cameron told reporters at his country residence, Chequers, that it was believed the explosive device intercepted at East Midlands Airport was "designed to go off on the aeroplane".
"We cannot be sure about when that was supposed to take place," he added.
"There is no early evidence that it was meant to take place over British soil, but of course we cannot rule it out."
The prime minister said the authorities had immediately banned packages coming to or through the UK from Yemen, and would be "looking extremely carefully at any further steps we have to take".
UK Home Secretary Theresa May said the government did not believe the plotters would have known the location of the device when it was planned to explode.
While details of the device found in Britain were not released, photographs emerged on the US media of an ink toner cartridge covered in white powder and connected to a circuit board.
The British government's remarks suggest the authorities in both the UK and the US remain uncertain about the precise targets and, indeed, aim of this latest apparent plot, BBC defence and security correspondent Nick Childs reports.
According to Dubai police, the explosives they found were also inside the toner cartridge of a printer, placed in a cardboard box containing English-language books and souvenirs.
The cartridge contained PETN and plastic explosives mixed with lead azide, they said. Lead azide is an explosive commonly used in detonators.
"The device was prepared in a professional manner and equipped with an electrical circuit linked to a mobile telephone [Sim] card concealed in the printer," the police said.
For US Homeland Security Secretary Janet Napolitano, the plot bore "all the hallmarks of al-Qaeda and in particular [AQAP]".
Unnamed US officials quoted by the Associated Press said al-Qaeda's explosives expert in Yemen, Ibrahim Hassan al-Asiri, was the likely suspect behind the bomb-making.
They said Mr Asiri had helped make the bomb used in the failed Detroit Christmas bomb attack and another PETN device used in a failed suicide attack against a top Saudi counter-terrorism official last year.
The White House has said Saudi Arabia provided information that helped identify the threat, while the UK's Daily Telegraph reported that an MI6 officer responsible for Yemen had received a tip-off.