The man, carrying a cocktail of explosives according to Swedish investigators, was only “a couple of hundred metres” from causing massive casualties, Bildt told BBC television Monday.
“He was heading into a place where if he had exploded all of the ordnance that he had with him… it would have been mass casualties of a sort that we have not seen in Europe for quite some time,” he told the programme Newsnight.
“We were extremely lucky… I mean minutes and just a couple of hundred metres from where it would have been very catastrophic.”
The bomber, whom investigators strongly believe was Taimour Abdulwahab, was the only person to die in Saturday’s attack. Two other people were injured when the bomber detonated a car before blowing himself up.
Bildt said that Sweden was working with other countries, including Britain and the United States, to figure out whether the bomber had any accomplices.
British police have been searching his house in Luton, just north of London, where he had been living with his family.
“It might be that he was operating on that particular night alone,” said Bildt.
“It might be that preparations and training and whatever was part of a wider network. But that is obviously something that the authorities are extremely keen to find out.”
Sweden’s chief prosecutor Tomas Lindstrand told reporters he was “98 percent” certain of the bomber’s identity, but was awaiting DNA test results for confirmation.
Investigators believed the bomber was a Swedish citizen who lived in Britain and that he had been bent on killing “as many people as possible”, he added.
And after an Islamist group said Abdulwahab had targeted Sweden because of its military presence in Afghanistan, Lindstrand warned that the bomber would likely have had accomplices.
In London, meanwhile, a spokesman for the city’s Metropolitan Police said officers had raided a property in nearby Luton late Sunday as part of the investigation.
Prosecutor Lindstrand sketched a similar scenario to reporters: “He had a bomb belt on him, he had a backpack with a bomb and he was carrying an object that has been compared to a pressure cooker.
“If it had all blown up at the same time, it would have been very powerful,” he said.
“This was during Christmas shopping in central Stockholm and he was extremely well-equipped when it came to bomb material…. It is not much of a stretch to say he was going to a place with as many people as possible.”
And while it had been established the suspect carried out the attack alone, investigators “have to assume he worked with several people,” Lindstrand added.
Abdulwahab, a father of three, would have been 29 the day after the blasts.
He was reportedly born in Iraq, but investigators said he became a Swedish citizen 18 years ago. He had never come to the attention of the security services, they added.
In Britain, the chairman of a mosque in Luton where the suspected bomber used to worship described Abdulwahab as a “bubbly” character.
He had been known for his hardline views before he “stormed out” for good when tackled about them in 2007.
“I had to confront him three or four times because his views were so extreme,” Qadeer Baksh told AFP.
“He was saying physical jihad was an obligation for all Muslims and saying that Muslim scholars are unreliable and untrustworthy because they are in the pockets of governments,” he added.
“I am shocked because I never imagined he would go this far.”
Luton has seen clashes between Islamic and far-right extremists in recent years.
In 2005 the four suicide bombers who killed 52 people on London’s transport system met up there to make their way into the capital.
An Islamist website, Shumukh al-Islam, posted a purported will by Abdulwahab which said he was fulfilling a threat by Al-Qaeda in Iraq to attack Sweden.
On Saturday Sweden’s Saepo intelligence agency and the TT news agency received an email with audio files in which a man believed to be the bomber is heard calling on “all hidden mujahedeen in Europe, and especially in Sweden, it is now the time to fight back.”
The message referred to the Swedish army’s presence in Afghanistan and to Swedish artist Lars Vilks, the object of numerous threats since his drawing of the Prophet Muhammad was first published in 2007.