"Norway is a substantial contributor to global development efforts, and wishes to join countries from Asia and other parts of the world in further refining the structure and mission of the AIIB," Foreign Minister Børge Brende said in a statement.
China has given other countries until March 31 to express interest in joining the project, which is aimed at financing infrastructure development in Asia.
The outcome of Norway's candidacy is uncertain, however. Beijing cut all high-level ties with Oslo after the Nobel Peace Prize went to Liu Xiaobo in 2010.
The Norwegian government has repeatedly maintained that the Nobel Committee is independent and makes its own choices, but the Chinese regime has torpedoed any attempts at normalising relations.
"The AIIB is an open and inclusive organisation and we welcome the participation of all parties to jointly promote infrastructure building in Asia," a Chinese government spokeswoman told reporters prior to Norway's
"We welcome countries in and outside the region to take an active part in the preparations for the establishment of the AIIB," she said.
Numerous countries, including Brazil, Britain, Egypt, France, Germany, Italy, Russia and Sweden have expressed interest in joining the AIIB. Japan and the US are however sceptical.
The new multinational lender is seen as a threat to the World Bank and the Asian Development Bank, two institutions that are heavily influenced by the US and Japan.
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Beijing said elsewhere on Tuesday that Taiwan would not be allowed to join the AIIB, citing its "One China" policy which sees the island as part of its territory awaiting reunification.
The AIIB, whose headquarters will be in Beijing, will initially have $50 billion (46 billion euros) at its disposal.
China is expected to foot the bulk of the initial money needed to get it started, with donations from other members set to increase the size of the overall fund to more than $100 billion.