"It is always nicer to say yes than no, but it is in our mandate to make tough decisions," the centre-right mayor Sten Nordin from the Moderate Party told Swedish news agency TT.
"This isn't a no to other Winter Olympics in the future."
The project had already been rejected by two of the Moderates' coalition partners, the Liberals and the Christian Democrats.
"Bidding for the Olympics in the current situation would entail too much speculation with taxpayers' money," Christian Democrat leaders Ewa Samuelsson and Erik Slottner said in a statement.
The Swedish Olympic Committee had submitted an application with a preliminary bid to the International Olympic Committee last November.
The preliminary bid was greeted with scepticism by the country's centre-right government.
"I think it's good to host big events but we're doubtful about the budget they've presented," sports minister Lena Adelsohn told daily Dagens Nyheter.
Located on low-lying land far from the mountains, the capital city planned to co-host events with Åre ski resort, about 500 kilometres to the north west.
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The host city will be elected at the 127th International Olympic Committee's session in Kuala Lumpur on July 31, 2015.
The other candidate cities are Oslo, Beijing, Krakow (with events held in other Polish locations and in neighbouring Slovakia), Lviv (Ukraine) and Almaty (Kazakhstan).
Sweden has only been an Olympic host nation once, hosting the 1912 Summer Olympics in Stockholm.