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The scandal first broke on Friday when Swedish trade union giant Kommunal, which also owns several properties in the capital was accused of renting out its apartments to labour movement bosses while refusing to release them to the public housing queue.
The Aftonbladet daily was the first Swedish newspaper to claim that Foreign Minister Margot Wallström was one of the left's "high-profile figures" who in deference to their positions were rented apartments in the Swedish capital, bypassing a wait of on average eight years faced by ordinary renters.
The 61-year-old Social Democrat insists she acted in good faith.
"I welcome an investigation. I have nothing to hide and it is good that this will get sorted out," she told news agency TT, adding: "I will continue to do my job."
Speaking to TT earlier this week, Sweden's Prime Minister Löfven defended his ministerial colleague.
He suggested Wallström was guilty of no wrongdoing, but that he was sorry the issue had arisen in the first place.
“I think it would have been better if she had sorted accommodation in a different way. There's no formal error, as far as I know, but it would have been better,” he said.
Magnus Isberg, a constitutional expert, told TT on Tuesday that there was nothing in Swedish law which suggested that a serving minister should be dismissed during a preliminary investigation such as the one currently being carried out.
"A preliminary investigation is not so terribly serious, although of course it's not so good for the government. But I find it hard to believe that this would lead to prosecution," he speculated.