Obama was informed about the NSA's tapping of Merkel's mobile phone already in 2010 by its director Keith Alexander.
The president "not only did not stop the operation, but he also ordered it to continue," Bild am Sonntag newspaper said quoting a high-ranking NSA official.
The White House later ordered the spy agency to prepare a detailed dossier on the chancellor.
President Obama did not trust Merkel and wanted to know everything about her, Bild said said quoting the official, who was not identified.
The agency also cracked the codes of a new supposedly tap-proof mobile phone she has been using since the middle of this year, the newspaper said.
This showed that the NSA continued its spying on the chancellor until very recently, it said.
Merkel's conversation from her office via fixed line phones, which she used to communicate with other world leaders, was secure from eavesdropping, the newspaper said.
A report today claimed that President Obama had assured chancellor Merkel during a telephone conversation last Wednesday that he was not aware of the NSA's spying on her.
Bild said President Obama's interest in information about Merkel was evident from the fact that intelligence gathered by the NSA did not go as usual to its headquarters in Fort Meade, in Maryland, but directly to the White House.
Another report in weekly news magazine Der Spiegel said NSA may also have spied on the entire government complex in Berlin from the nearby American embassy.
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