"You can never be confident that you will survive for four years," Solberg told AFP on Tuesday.
"There was a lot of speculation that this (government) would not last after the last election in 2013. We have managed to do this and I think it's possible to do it for the four next years," she said.
The popular and experienced 56-year-old is the first Conservative in oil-rich Norway to win a second straight mandate in more than 30 years.
In Monday's nail-biting election, her coalition -- made up of the Conservatives and the populist anti-immigration Progress Party – and two smaller centre-right allies took home a thin majority of 89 of the 169 seats in parliament.
The Conservatives campaigned on a vow to pursue further tax cuts to bolster the economy.
The opposition, led by Labour leader Jonas Gahr Støre, meanwhile wanted to raise taxes, especially for the richest, seeking to reduce inequalities and beef up the Norwegians' cherished welfare state.
Credited with successfully steering the country -- Western Europe's biggest crude producer -- through the oil industry slump and the migrant crisis, Solberg now looks set to have her work cut out, simple arithmetic shows.
The right wing bloc lost seven seats in the new parliament. It will need to stand more united than ever to govern -- and that is easier said than done.
Until now, Solberg's coalition had held a minority in parliament and needed the support of only one of the two smaller centre-right parties – the Christian Democrats or the Liberals -- to pass legislation.
But now Solberg needs the support of both parties to do that, and they have both expressed growing dissatisfaction with the populists on issues such as the climate and immigration.
Contrary to four years ago, the Christian Democrats have already ruled out any formal alliance with a coalition that includes the Progress Party – a very likely member of Solberg's government.
"We can't provide any guarantee for the next four years," the head of the Christian Democrats, Knut Arild Hareide, warned.
Without a formal cooperation agreement with the Christian Democrats and the Liberals, Solberg will have to engage in tricky negotiations on each issue to obtain the support of the centre-right, which has refused to give her a blank cheque.
Concessions and compromises will be necessary, leading tabloid Dagbladet to headline Tuesday's frontpage "Bittersweet Victory".
As soon as the election results were in late Monday, Solberg invited the right wing parties to find a way forward.
"We will talk to the two partners the coalition has had in parliament, and we'll try to reach an agreement with them. And we'll see where we go from there," Solberg told AFP, noting that the two parties had more influence working with the government than in opposition.
Before the shape of the next government had even taken form, questions were already being raised about its chances of survival.
"It's not a given that they will last four years," warned Audun Lysbakken, head of the Socialist Left party, one of the few winners in the election even though it remained in the opposition.
Knut Heidar, a political science professor at University of Oslo, also said it was "unlikely the government would survive four years."
"The immigration issue, or maybe the urban-rural relations, will push the Christian Democrats to topple it," he told AFP.
Kåre Willoch, the only other Conservative prime minister to win a second straight mandate in the post-war period, never made it to the end of his second term.
His government lost a vote of no-confidence in 1986, just over a year after his re-election.
Ultimately, it was not so much the right that won Monday's election – all rightwing parties lost seats in parliament -- but rather the left that lost.
While Labour remains the biggest party in the country, as it has been since the 1920s, it was seen losing six seats in parliament.
"This is a big disappointment for Labour," Støre told his supporters late Monday, refusing nonetheless to give up the party leadership.