Polls were scheduled to open at 9am local time for the second and final day of voting.
The latest opinion polls from TV2 shows that the Labour Party (AP) has a 28.1 per cent lead, while the Conservatives (Høyre) are at 23.8 per cent.
Mrs Solberg’s centre-right bloc is expected to gain 85 mandates and Mr Støre’s opposition 84 of the 169 seats in parliament.
Norway uses a modified proportional representation system in which 150 MPs are directly elected in the country’s 19 constituencies.
The remaining 19 seats will be distributed proportionally to parties that clear a 4 per cent vote threshold.
Five parties, two on the left, two on the right and the Green Party, are all close to this threshold according to opinion polls.
Professor Toril Aalberg of the Norwegian University of Science and Technology said: “This can tip the scale one way or the other.”
Taxes, public services and oil exploration are among key issues in the election.
Mrs Solberg plans to cut taxes if her coalition returns to power, while Mr Støre wants tax hikes to pay for better public services.
Mr Støre, who cast his ballot on Sunday in Oslo, expressed confidence his party could rally voters in the final days of the election.
He told NTB: “I have butterflies in my stomach and I am very excited. I have a good feeling in light of the last days’ mobilisation.”
The Labour Leader, who was out campaigning yesterday, told reporters: “Thousands of voters are still undecided.”
The outcome of the election is expected to have a huge impact on Norway’s oil industry as one or more of the smaller parties in each of the coalitions are seeking to impose limits oil exploration in Arctic waters off Norway’s northern coast.
The Greens want to end all oil exploration, having expressed concerns over climate change and pollution.
Finance Minister Siv Jensen, of the right-wing Progress Party, told TV2 on Sunday: “It’s exciting, and extremely close, so it’s important for all to vote. Every ballot counts.”
Mrs Solberg said on Thursday: “I am humble about the election. It is the voters who decide, but I have good faith, because we’re getting so much good feedback at the moment.”
The prime minister was out campaigning in Ski, Oslo and Bergen yesterday.
She told NTB: “It’s important to get people to vote. They will have to put up with us until the election day.
As many as 3.67 million of Norway’s 5.233 million strong population are registered to vote, and one million people have for the first time voted ahead of election day.
Exit polls and forecasts based on early votes will be released today at 7pm GMT, with most ballots to be counted in the following hours.
In an exceptionally tight race the results could be published late Tuesday.