“This strikes at the democratic node of Europe. We're mourning with Brussels,” said Löfven as he addressed a press conference in Stockholm, held just hours after a series of blasts in the Belgian capital – home to some of the EU's top institutions – claimed at least 30 lives and injured hundreds.
The centre-left leader said a number of measures designed to prevent attacks in Sweden, for example making it illegal to take part in terrorist activities abroad, would soon come into effect.
But he added that an open society could never completely protect itself from terrorism.
“We can never guarantee that it won't happen, no. But it's our obligation to do everything we can to prevent it,” said Löfven at the press conference, which started almost 45 minutes behind schedule.
Sweden agreed after last year's Paris attacks to help France fight Isis militants in Syria. Löfven pledged on Tuesday that his Social Democrat-Green government would also be prepared to assist Belgium, although he said he would not comment on what such support would look like until a request was made.
The attacks in the Belgian capital come three weeks after Sweden lowered its national terror threat level back down to three on a five-point scale, after raising it to a record four ('high') in November.
Löfven said he trusted the Säpo security police's judgment in assessing threats to Sweden, after it said earlier on Tuesday that Sweden's terror alert would for now remain at a steady level-three ('elevated').
Swedish leader Stefan Löfven. Photo: Fredrik Sandberg/TT
Several other Swedes joined the Prime Minister in paying tributes to victims and denouncing the attacks.
Slightly worrying, to put it like that, if the city of EU institutions turns into some sort of war zone.- Carl Bildt (@carlbildt) March 22, 2016
“Horrifying attacks in Brussels, on victims and families but also on our open society and way of life. Terrorism must be fought forcefully,” wrote Anna Kinberg Batra, leader of Sweden's biggest opposition party in parliament, the centre-right Moderates, on Twitter.
Shocked by attacks in Brussels. We can not accept terrorism in our open societies.- Margot Wallström (@margotwallstrom) March 22, 2016
“We are shaken after the attacks but won't let terror win,” tweeted Fredrik Federley, member of the centre-right Centre Party and one of Sweden's most high-profile representatives in the European Parliament, which was put in lockdown by police immediately following the attacks.
Meanwhile his colleague Soraya Post, who represents Sweden's Feminist Initiative party in the European Parliament, tweeted a picture of the Maelbeek metro station, where dozens died on Tuesday morning. “It's a crater. Great sorrow. Strength to [the victims'] families,” she wrote.
Utsikten från parlamentet. T-banestationen Maelbeek är en krater. Stor sorg. Styrka till alla anhöriga. pic.twitter.com/JPiSdvu6tT- Soraya Post (@SorayaPostFi) March 22, 2016
Jonas Sjöstedt, the leader of Sweden's Left Party, wrote: "Terrible and cowardly terror acts in Brussels. I think of everyone who's been affected. Let's fight terror with firmness and democracy."
Fruktansvärda och fega terrordåd i Bryssel. Jag tänker på alla som drabbats. Låt oss bekämpa terrorn med fasthet och demokrati.- Jonas Sjöstedt (@jsjostedt) March 22, 2016
And Jimmie Åkesson, who heads the right-wing Sweden Democrats, commented in a Facebook post: "Brussels has today been hit by a terrible incident with both dead and injured. Let all our thoughts go to the victims and their families."