Norwegians are to vote in what is expected to be a closely fought poll between the prime minister`s Labour Party and the centre-right opposition, BBC.
Jens Stoltenberg, in power since 2005, has emphasised his success in guiding Norway through the economic crisis.
The world`s fifth biggest exporter of crude oil experienced only a brief recession and has Europe`s lowest unemployment rate.
His main challenger is Siv Jensen who leads the right-wing Progress Party.
She has campaigned on a platform of lower taxes and tightening immigration. Currently, more than 10% of Norway`s population is of foreign origin with the largest groups of asylum seekers coming from Afghanistan, Iraq, Somalia and Eritrea.
Norwegians - who pay some of the highest taxes on the planet - have high demands of their public services and often complain about long hospital waiting lists for non-emergency operations and bad roads.
But in a debate on Sunday, Mr Stoltenberg said voters could not expect a "social-democratic paradise".
Ms Jensen hit back saying: "I believe you won`t build a social-democratic paradise by Tuesday because you`ve been at it since the war and you still haven`t managed it."
The Progress Party has pledged to spend more of the country`s vast oil wealth at home and to broaden privatisation in both the health and education sectors.
But analysts say it is unlikely that her party would be in a position to govern even if centre-right parties won a majority of the votes because of a lack of unity between them.