A popular and experienced 56-year-old politician, Solberg 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 mildly populist anti- immigration Progress Party -- and two smaller centre-right allies took home a thin majority of 89 of the 169 seats in parliament.
"We received a new mandate for four more years because we delivered results, we delivered what we promised," Solberg told cheering supporters late Monday as she claimed victory.
The opposition, led by Labour leader Jonas Gahr Store, wanted to raise taxes, especially for the richest, to reduce inequalities in society and beef up the Norwegians' cherished welfare state.
More From This Section
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 for her, simple math shows.
With 95 per cent of votes counted on Tuesday, the rightwing bloc was shown losing seven seats in the new parliament. It will need to stand more united than ever to govern -- and that is easier said than done.
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.
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 rightwing parties "to talks where we will clarify how to continue our cooperation.