AFP - Finland is in mourning after a jealous ex-lover shot dead his former girlfriend and four of her work colleagues in the latest armed rampage which has reignited debate on the country's gun controls.

Ibrahim Shkupolli ended his killing spree on Thursday by turning his weapon on himself, bringing the overall toll from the tragedy in the normally sleepy Helsinki suburb of Espoo to six.

As relatives of the victims tried to come to terms with their loss, Prime Minister Matti Vanhanen acknowledged it raised new questions about firearms laws.

"The incident draws attention to the large amount of handguns in our country," Vanhanen said in a statement.

"Broad-based cooperation within our society is necessary to avoid such tragedies in the future."

Finland, one of western Europe's most sparsely populated countries with a long tradition of hunting, has one of the largest per capita gun ownerships in the world.

But debate about the level of gun ownership has become a hot political topic in the wake of two shootings at schools in 2007 and 2008 which left a total of 18 pupils and staff dead as well as the two shooters.

A new firearms law, intended to tighten up licensing requirements, is due to be put before parliament in the spring.

Investigators said that the gun used by Shkupolli, 43, was not licenced.

The 43-year-old was fined by the Helsinki District Court in 2007 for firearm violation for illegal possession of a 9 mm handgun and ammunition.

The Espoo District Court had also fined Shkupolli for illegal possession of a 7.65 calibre handgun and ammunition in 2003.

Having expressed his condolences to the victims' families, Vanhanen said that "the background of the events will be examined, especially the background and origin of the unlicensed gun".

Newspapers asked pointed questions about how easily the shooter had been able to get his hands on a weapon even though alarm bells had already been well and truly sounded.

As well as his run-ins with the law over illegal firearms, he was also the subject of a restraining order issued by a court over harassment of his ex-girlfriend.

Police acknowledge that lessons had to be learned but nevertheless defended their performance when asked if they could have done more to prevent the shootings.

"In retrospect, one could have of course assessed the situation in different ways, but according to the knowledge of that moment the police and the justice system had given him the necessary attention," Inspector Tero Haapala told the private MTV3 news channel.

Haapala said that investigators believed that Shkupolli's actions were prompted by jealousy.

"A strong line of investigation is the jealousy of the couple in the relationship which expressed itself so sadly and seriously," he said.

Haapala said that Shkupolli appeared to have deliberately sought out his victims in the mall, all of whom worked at the same supermarket where the former girlfriend worked.

"The injuries of the victims indicate that the shooter wanted to shoot just them. There were no bullets shot in the direction of bystanders," he said in comments to the online edition of the Helsingin Sanomat newspaper.

Witnesses said the shooting sparked panic among the around 4,000 New Year's Eve shoppers in the mall in mid-morning, with many charging headlong for the exit.

Armed police and medics who rushed to the scene found the bodies of three men and a woman at the Prisma supermarket and then later found the ex-girlfriend's body at her home.

After an extensive search of the mall proved fruitless, officers issued a photograph of Shkupolli and called on the public to help find him. His body was found several hours later.