Prime Minister Lars Loekke Rasmussen says he will resign on Thursday from the post he has held since 2015.
Polling stations open at 8 am (0600 GMT) and close at 8 pm, followed immediately by two exit polls. The focus will be on challenges in the Nordic country's welfare model and on two new far-right anti-immigrant parties.
A body retrieved from the Thames river is believed to be that of a French national who was killed in the attack over the weekend.
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