Støre made his comments as parliament met behind closed doors on Monday over a 2016 Norwegian General Auditor (Riksrevisjonen) report on terror contingency plans which was made confidential by Prime Minister Erna Solberg's government.
The report stated that Norway's police and military had insufficient capability with regard to securing public buildings, calling this a “very serious” problem.
The Norwegian General Auditor report was initially intended to be published before being made confidential by the Ministry of Defence. A summary of it was later leaked to the Dagens Næringsliv newspaper.
"I think... this secrecy is a shame for the government," Støre told NRK.
“This secrecy creates the impression that the government is trying to cover up its own problems,” the Labour leader continued.
Parliament is scheduled to hold a behind-closed-doors meeting on security and emergency response on Monday, reports the broadcaster, with MPs required to switch off mobile phones and other devices before entering the sound-proof chamber. Several floors of parliament's Stortinget building have also been closed off.
A private parliamentary meeting of this kind has not been held for 25 years, reports NRK.
The meeting was called after the government and Defence Miniser Ine Eriksen Søreide declined to meet a parliamentary request to publish confidential parts of the audit office's report on security of important buildings and infrastructure.
While the government says that publicising the report may put at risk Norway's ability to defend itself militarily, opposition parties are critical of crucial contingency plans for terror being discussed behind closed doors.
“This is serious, it brings the legacy of the 22nd July [terror attacks carried out by Anders Behring Breivik, ed.] at risk. It breaks the line of openness that has been followed since 22nd July,” Støre said.
Defence minister Søreide told NRK that the issue was complex.
“Security in Norway is not just objective in terms of securing buildings, but also information security. This is also about information security,” she said.