Just two months after raising its threat level, Sweden was in shock on Tuesday over the killing of two of its football fans in a "terror attack" targeting Swedes in Brussels.

The country's worst fears came true when a suspect of Tunisian origin living illegally in Belgium gunned down two Swedes and injured a third on Monday evening on a street, just before the start of a Belgium-Sweden international football match. 

The Swedish government, football fans and the public expressed their devastation over the attack.

"Sweden has in modern times never been under as big a threat as now," Prime Minister Ulf Kristersson told reporters in Stockholm.

"Every indication is that this is a terror attack, targeting Sweden and Swedish citizens, just because they are Swedes," he said, adding he felt an "unfathomable sadness".

In August, Sweden's intelligence service Sapo raised its threat level to four on a scale of five after a series of Koran burnings across the country -- most notably by an Iraqi Christian -- sparked outrage in the Muslim world and made the Scandinavian country a "prioritised target".

"It was risks like this that were the reason Sapo this summer raised the threat level from three to four," Kristersson said.

"Now we know with chilling clarity that there was cause for the concern that they and we in the government described," he added.

"We are living in dark times."

In a social media post after the killings, the gunman had boasted of being inspired by the Islamic State extremist group.

Several Belgian media named the suspect as Abdesalem L, aged 45.

Kristersson said he had been informed that the suspect had "spent time in Sweden", but provided no further details.

Following the attack, Sweden's foreign ministry advised Swedes abroad "to observe increased caution and heightened vigilance, and to heed the advice of local authorities."

The prime minister vowed "to protect our open, democratic society".

"They want to scare us into silence ... That's not going to happen," he said.

- 'Not used to being targets' -

However, he stressed "this is a time for more security, more caution, more vigilance."

"We simply can't be naive."

The head of security for Sweden's football association, Martin Fredman, told AFP he had advised Swedish football fans in Brussels on Monday "to pack away their yellow-and-blue jerseys" -- so they wouldn't be potential targets -- "and fly home".

He said it was an unusual situation for Swedes.

"We're not used to being targets."

The match was halted at half-time and Swedish fans were ordered to stay put for several hours until they could be evacuated safely with police escorts.

Andreas Matz, a Swedish journalist covering the match in the arena, told newspaper Dagens Nyheter he had always associated Sweden's yellow team jerseys with "such joy, excitement and celebrations".

"Now in the future I'm always going to think, 'damn, are you really going to wear the jerseys?'," he said.

"It's so unbelievably awful that you can be a target because you're wearing the yellow jersey."

Kristersson said the measure was a precautionary one for now, "but I don't want Swedes to have to walk around hiding the fact that they are Swedes."

Jorgen Axelsson, a fan who had travelled to Brussels with a group of friends to watch Monday's match, told daily Aftonbladet he was stunned by the attack.

"Regardless of which country you represent you should be able to wear your team's jersey," he said.

At a press conference late Monday, Sweden coach Janne Andersson said he reacted with disbelief when he received the news at half-time.

"It was totally unreal. What kind of world are we living in today," he said.

bur-po/cw