In remarks published in German, Snowden said an NSA department known as the foreign affairs directorate coordinated work with foreign secret services.
The partnerships are organised so that authorities in other countries can "insulate their political leaders from the backlash" if it becomes public "how grievously they're violating global privacy," he said.
The interview was conducted by US cryptography expert Jacob Appelbaum and documentary filmmaker Laura Poitras using "encrypted emails shortly before Snowden became known globally for his whistleblowing", Spiegel said.
On cooperation with Germany's BND foreign intelligence agency, Snowden said the NSA provides "analysis tools" for data passing through Germany from regions such as the Middle East.
The US government has revoked the passport of Snowden, a former NSA contractor who is seeking to evade US justice for leaking details about a vast US electronic surveillance programme to collect phone and Internet data.
He has been stranded at a Moscow airport for two weeks but three Latin American countries have now offered him asylum.
His claims about widespread US spying on Western partners have sparked uproar among European allies in particular and threatened to derail talks on the world's largest free-trade zone due to start on Monday.
German chancellor Angela Merkel spoke with US President Barack Obama on Wednesday and agreed to a "high-level meeting" between US and German security officials in the coming days to address intelligence matters.