With 99.7 percent of the votes counted from Monday's election, the four right-wing parties were projected to win 96 seats and the center-left coalition was projected to claim 72 seats, the Norwegian version of The Local reported Tuesday.
Eighty-five seats are needed to secure a majority in parliament.
"Today you have helped to make history," Conservative leader Erna Solberg said. "Now it's our job to really do what we have promised."
In his concession speech Monday night, Prime Minister Jens Stoltenberg said he would leave office after presenting the next budget.
"The result must be viewed in light of the fact that we have been eight years in government," Stoltenberg said.
Siv Jensen, leader of the populist Progress Party, said her party may be willing to soften some of its tough positions on immigration to achieve a coalition among the four right-wing parties.
"We must be tough bargainers, but we must also be realistic bargainers," she said.
Bernt Aardahl, a professor of politics at the University of Oslo, said before Monday's elections the outcome of coalition negotiations would be unpredictable, The Local reported.
"I think the negotiations after the elections will be tough, and it is still an open question over whether it will be a four-party government or a two-party government," he said. "If the Progress Party will be willing to modify their anti-immigration position in exchange for other policy goals that they have, that might simplify negotiations."