Fresh reports in German media based on leaked US intelligence documents are prompting damaging new questions about the extent of US surveillance.
Der Spiegel suggests the US has been spying on German Chancellor Angela Merkel’s mobile phone since 2002.
Another report says Mr Obama was told in 2010 about the surveillance and failed to stop it.
The spy row has led to the worst diplomatic crisis betweeen the two countries in living memory.
Leaked documents say a US listening unit was based in its Berlin embassy – and similar operations were replicated in 80 locations around the world.
The German interior minister has been quoted as saying such an operation, if confirmed, would be illegal.
On Friday, Germany and France said they wanted the US to sign a no-spy deal by the end of the year.
As well as the bugging of Merkel’s phone, there are claims the NSA has monitored millions of telephone calls made by German and French citizens.
Der Spiegel claims to have seen secret documents from the National Security Agency which show Merkel’s number on a list dating from 2002 – three years before she became chancellor.
This might indicate that there was extensive bugging of the phones of prominent people, says the BBC’s Stephen Evans in Berlin.
German Chancellor Angela Merkel checks her mobile phone during a session of the Bundestag (30 November 2012) Angela Merkel is known for her avid mobile phone use
The nature of the monitoring of Mrs Merkel’s mobile phone is not clear from the files, Der Spiegel says.
For example, it is possible that the chancellor’s conversations were recorded, or that her contacts were simply assessed.
Merkel phoned the US president when she first heard of the spying allegations on Wednesday.
President Barack Obama apologised to the German chancellor and promised Mrs Merkel he knew nothing of the alleged phone monitoring and would have stopped it if he had, Der Spiegel reports.
But on Sunday Bild newspaper quoted US intelligence sources as saying NSA head Keith Alexander personally briefed the president about the covert operation targeting Mrs Merkel in 2010.
“Obama did not halt the operation but rather let it continue,” the newspaper quoted a senior NSA official as saying.
Her number was still on a surveillance list in 2013.
Germany is sending its top intelligence chiefs to Washington in the coming week to “push forward” an investigation into the spying allegations, which have caused outrage in Germany.
Criminal investigation?
The documents seen by Der Spiegel give further details about the NSA’s targeting of European governments.
A unit called Special Collection Services, based on the fourth floor of the US embassy in Pariser Platz in Berlin, was responsible for monitoring communications in the German capital’s government quarter, including those targeting Mrs Merkel.
Germany’s Interior Minister Hans-Peter Friedrich told Bild that running such an operation on German soil would be illegal under German law, and adds that those “responsible must be held accountable”.
Similar listening units were based in around 80 locations worldwide, according to the documents seen by Der Spiegel, 19 of them in European cities.
If the existence of listening stations in US embassies were known, there would be “severe damage for the US’s relations with a foreign government,” the documents said.
Merkel – an Americophile who was awarded the US Presidential Medal of Freedom in 2011 – is said to be shocked that Washington may have engaged in the sort of spying she had to endure growing up in Communist East Germany.