Since the Cold War ended more than 20 years ago, NATO had tried to build a working, practical relationship with Russia but all that had now come to nothing, said Rasmussen.
Through its actions in Ukraine, Russia "has broken the rules and eroded the trust," he said.
Rather than NATO being the problem, as Russia charges, it was Moscow's "illegal actions in Ukraine which pose a threat to the international order," he said.
With no change in Russia's behaviour, NATO had no option but to maintain the suspension.
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"There will be no business as usual... Until Russia comes back into line with its international obligations," Rasmussen said.
He reiterated that Russia had to stop de-stabilising Ukraine, and end what the West sees as support for pro-Moscow rebels there.
The NATO foreign ministers meeting is dominated by the crisis in Ukraine where a Kiev government peace plan and peace plan was in the balance today after rebels shot down a Ukrainian helicopter yesterday.
Moscow said the West should be paying attention to what Putin was saying and doing to help the resolve the crisis but the NATO meeting heard repeated calls for Russia to do more or face the prospect of tougher sanctions.