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She had been undergoing surgery for most of the night for injuries to her chest, stomach and arms, but doctors were unable to save her.
Her death has shocked the nation, and raised questions about Sweden's long tradition of accessibility for politicians. Like many officials, Anna Lindh did not use a bodyguard.
The attack took place yesterday at about 1600 local time (1400 GMT) when Mrs Lindh was shopping with a friend in the Nordiska Kompaniet shop in Stockholm.
A man described as tall, wearing a peaked cap and camouflage jacket, stabbed her several times before running off.
Mourners have been arriving all day to lay flowers on the pavement outside the shop.
National flags have been flying at half-mast, and a special service was held in Uppsala cathedral this evening.
The motive for her killing remains unknown.
However, there is speculation that it could be linked to her vigorous campaigning for a "yes" vote in a referendum on whether Sweden should join the euro. The vote is due to take place in three days' time.
Anna Lindh, who was married with two children, had been an active politician since her early twenties.
She had a meteoric rise through the ruling Social Democratic Party, and became foreign minister in 1998, at the age of 41.
Her solid reputation and her widespread popularity led her to be widely tipped as a possible successor to Prime Minister Goran Persson.
Mr Persson described her death as "beyond belief" and said it had hurt Sweden's open and democratic society.
"Sweden has lost one of its most important representatives," he said. "It feels unreal, it is difficult to truly understand."
Security has been tightened around government buildings, but police said there was as yet no evidence of a political motive.
Her death has also stirred memories of the murder of Swedish Prime Minister Olof Palme, who was shot in the back, coincidentally on the same street as the attack on Mrs Lindh, as he walked home from the cinema with his son and his wife in 1986.
Police initially arrested the wrong man, but then detained 25-year-old Mijailo Mijailovic, the son of Serbian émigrés. He had a history of psychiatric problems.
At his trial, in January 2004, he said he was directed to stab Mrs Lindh by voices in his head.
But psychiatric tests carried out after the end of the trial declared him sane at the time of the killing. As a result, he was sentenced to life in prison for murder.
In July 2004 an appeals court overturned the verdict and, in a highly controversial decision, ordered him to be sent to a closed psychiatric ward instead.
An inquiry into the state of Sweden's psychiatric care system is now under way.
In the euro referendum, held as scheduled three days after Anna Lindh's death, there was a decisive "no" vote against taking the euro as Sweden's currency.
Despite fears of a tightening of security following the murder, Sweden has fiercely stood by its prized open society, and the people still have direct access to their politicians.
But Laila Freivalds, Mrs Lindh's successor as foreign minister, no longer travels to work by train on her own.
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