Four people, including the attacker, were killed and some 40 injured in Wednesday's attack, in which a man mowed down pedestrians with a car and then fatally stabbed a police officer outside the parliament building in London before being shot dead.
“What has happened in London is atrocious, and our thoughts are with the victims, their families and the British people,” said Löfven, quoted by Swedish tabloid Expressen.
He added that regardless of the identity of the perpetrator, “this shows the vulnerability of all societies, and the extreme importance of being prepared for unforeseen attacks”.
Foreign Minister Margot Wallström tweeted: “My thoughts are with the UK and victims of the horrific attack at Westminster, the heart of British democracy.”
My thoughts are with the UK and victims of the horrific attack at Westminster, the heart of British democracy.
— Margot Wallström (@margotwallstrom) March 22, 2017
Terrible events in London today. My thoughts are with the victims of the #Westminster attack and the people of the UK.
— Torbjörn Sohlström (@sohlstromt) March 22, 2017
Around 90,000 Swedes live in Britain, according to the Swedes Worldwide organization, but the Swedish foreign ministry said on Thursday morning that none of its nationals appeared to be among the many injured.
“We have no information indicating that at the moment,” a spokesperson told The Local, adding that they had also had no calls from concerned people unable to reach their friends or relatives in London.
The attack unfolded on Wednesday across Westminster Bridge in the shadow of Big Ben. The attacker's car struck pedestrians before crashing into the railings surrounding the heavily-guarded Houses of Parliament.
The assailant then ran through the gates brandishing a knife and stabbed a 48-year-old policeman to death before being shot dead by another officer.
UK defence secretary Michael Fallon said on Thursday morning that British authorities were working to find out more about the man's background and potential associates.
“Their working assumption is this is linked to Islamic terrorism but they don't yet know and the investigation – and it is a very large investigation – has been under way since it happened,” he was quoted by The Guardian as telling Radio 4.