By Johnny Cotton

BRUSSELS Sweden's Prime Minister Ulf Kristersson and his Belgian counterpart Alexander De Croo paid tribute in Brussels on Wednesday to the victims of Monday's attack by a gunman in which two Swedish football fans died and one was injured.

Kristersson said on Tuesday that the attack in the Belgian capital by a 45-year rejected asylum-seeker from Tunisia showed the European Union must bolster security at its border and within the region to better protect itself.

On Wednesday, at the site where the gunman shot the Swedish football fans, Kristersson, a Swedish team football scarf around his neck, and De Croo, holding a Swedish team jersey, took part in a brief ceremony, laying wreaths for the victims after listening to a sad piece played on a cello.

They also laid the scarf and jersey among the flowers.

The gunman suspected of the killing died on Tuesday after being shot by police in a cafe.

He identified himself as a member of Islamic State and claimed responsibility for the attack in a video posted online. He called himself Abdesalem Al Guilani. Belgian state broadcaster RTBF named him as Abdesalem Lassoued.

Islamic State claimed responsibility for the attack.

The EU executive was due later on Wednesday to propose additional measures to strengthen security in Europe after the attack by the suspected gunman who earlier lived in Italy and Sweden underlined security gaps and failed returns policies.

He arrived in the EU via Italy's Lampedusa island in 2011, two Italian government and security sources have said.

He was identified in 2016 by police in Bologna as a subject at risk of Islamist radicalisation and came under observation by intelligence services.

The EU has for years tried and failed to overhaul its troubled migration system.

The shooting came at a time of heightened security concerns across much of Europe linked to the Israel-Hamas conflict, but prosecutors said the gunman appeared motivated more by Koran burnings in Sweden.

In August, Sweden raised its terrorism alert to the second-highest level and warned of an increase in threats against Swedes at home and abroad after burnings outraged Muslims and drew threats from jihadists.

The victims were men aged respectively around 60 and 70, Sweden's foreign ministry said.

"We are united in our fight against radical Islamist extremism," Sweden and Belgium's foreign ministries said in a joint statement.

(Reporting by Johnny Cotton, additional reporting by Marine Strauss, Anna Ringstrom, Gabriela Baczynska; Writing by Ingrid Melander, editing by Emelia Sithole-Matarise)