Rune Berglund Steen, who is head of the NGO, also said the lack of diversity represented a "democratic problem".
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"Even Trump's government has more people with minority ethnic backgrounds than the Norwegian [government]," Steen, who was speaking to broadcaster NRK, said.
Among the 68 ministers and secretaries presented by Solberg as she unveiled the new government on Wednesday, only two appear to be of minority background, according to NRK -- State Secretary Anne Karin Olli, who is of indigenous Sami heritage, and German-born Rebekka Borsch.
"This is a democratic problem. Those in power must reflect the general population and it is very serious that this is not the case in the extended government," Steen told NRK.
According to Statistics Norway, over 800,000 foreign or Norwegian-born people in Norway, which has a total population of around 5.2 million, have foreign-born parents.
"I am disappointed with the composition of the government. It is important for minorities to be represented, including amongst those who lead the country. This is connected to identity and confidence in the system. This sends an unfortunate signal," Sylo Taraku of Norwegian thinktank Agenda told NRK.
Minister of Education and Integration Jan Tore Sanner said the criticism was unjustified.
"Many things must be taken into consideration when a new government is formed. The most important is the policies that will be followed, regardless of which background one has," Sanner told NRK.
Steen said to the broadcaster that diversity was healthy in politics.
"Political outcomes are also affected by which people are involved and what backgrounds they have. It is clear that people with minority ethnic backgrounds have different experience when it comes to, for example, creating inclusive policies," he said.