German newspaper Bild am Sonntag yesterday quoted Interior Minister Hans-Peter Friedrich as saying the allegations have "shaken" Berlin's trust in Washington, a longtime ally.
Mr Friedrich told the newspaper: "If the Americans intercepted mobile phone communications in Germany, they broke German law."
That would be an "unacceptable violation of German sovereignty."
Bild am Sonntag quoted an unnamed official of the US National Security Agency as saying President Barack Obama received an NSA briefing in 2010 informing him that US spies were monitoring Chancellor Merkel's mobile communications.
The newspaper's source said Mr Obama allowed the operation to continue.
Mrs Merkel complained about the alleged NSA surveillance of her communications in a phone call to Mr Obama on Wednesday.
Her office said she told Mr. Obama that if such practices occurred, they represent a "grave breach of trust."
The White House said it is not monitoring Mrs Merkel's mobile phones and will not do so in future. But it did not comment on whether the NSA spied on her devices in the past.
The Bild am Sonntag report said the NSA allegedly bugged a mobile phone used by Mrs Merkel to conduct the business of her Christian Democratic Union party.
It also said it bugged a second supposedly secure device that she began using in the middle of this year.
The newspaper said the only phone of Mrs Merkel's that the NSA could not access was the land-line in her office.
In a separate weekend report, German weekly Der Spiegel said the NSA might have been bugging Mrs Merkel's mobile phone as early as 2002, when she served as opposition leader. She took office as Chancellor in 2005.
Former NSA contractor Edward Snowden leaked documents earlier this year purporting to show sweeping US surveillance of internet searches and telephone records of US citizens and world leaders. The revelations have sparked outrage globally.
Germany is working with Brazil on a draft UN General Assembly resolution to guarantee privacy in electronic communications.
UN diplomats say it would call for extending the International Covenant on Civil and Political Rights to internet activities, but would not mention the United States.
On Saturday protesters marched on Capitol Hill in Washington to protest against the US government's programmes of online surveillance.
Marchers carried signs reading: "Stop Mass Spying," "Thank you, Edward Snowden" and "Unplug Big Brother" as they gathered at the foot of the Capitol to demonstrate against the online surveillance by the NSA.
Estimates varied on the size of the march, with organizers saying more than 2000 attended.
The march attracted protesters from both ends of the political spectrum as liberal privacy advocates walked alongside members of the conservative Tea Party movement.