The decision brings an end to Solberg's ambition to bring the smaller and more centrist Liberal and Christian Democrat Parties into a four-party coalition, despite more than twelve days of tough negotiations.
It also marks the start of two-way talks with the Progress party, which promise to bring it, along with its controversial policies on Norway's oil fund, immigration and other issues, into government for the first time.
"Although we have had constructive conversations and got close to an agreement in several areas, the Christian Democrats and the Liberals are not now ready to be part of the government," Solberg said.
The four parties have however signed an agreement which gives some of the policy ambitions of the two minor parties a place in the government's programme, in exchange for their support on other issues.
Progress party leader Siv Jensen thanked the three other party leaders for an "an incredibly good climate" in the discussions.
"It has been a pleasure. This agreement is historic, both for Norwegian policy and for Progress," she said.
Frank Aarebrot, professor of politics at Bergen University said that operating as a minority government with the Progress party would be difficult.
"As I see it, a four-party government would have been best for Erna Solberg and the Conservatives," he told Aftenposten. "It would have been best because it would have had a solid majority in parliament. Now, she must first compromise in secret with Progress, and then she must go to Parliament and compromise once again."
In exchange for their support, the the Christian Democrats and Liberals won:
An amnesty for children of asylum seekers who have had their applications refused, so that they can remain in Norway
A moratorium on oil drilling in new, environmentally sensitive areas such as the Lofoten Islands
– a new emphasise on the teaching of Christianity in schools, so that it must make up at least 55 percent of the teaching on religion, philosophy and ethics
– a waiver allowing doctors to refuse to perform some operations (IE abortions) on moral grounds.