The US has been spying on German Chancellor Angela Merkel's mobile phone since 2002, according to a report in Der Spiegel magazine.
The German publication claims to have seen secret documents from the National Security Agency which show Mrs Merkel's number on a list dating from 2002 - before she became chancellor.
Another report says Mr Obama was told in 2010 about the surveillance.
Meanwhile Washington has seen a protest against the NSA's spying programme.
Several thousand protesters marched to the US Capitol to demand a limit to the surveillance. Some of them held banners in support of the fugitive former contractor Edward Snowden, who revealed the extent of the NSA's activities.
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.
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.
Mrs 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.
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 Mrs Merkel's phone, there are claims the NSA has monitored millions of telephone calls made by German and French citizens.
The documents seen by Der Spiegel give further details of 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".
A criminal investigation would take the current scandal out of the hands of diplomats and politicians, and so make it harder to control politically, says the BBC's Steve Evans in Berlin.
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.
The US government had a second German spy base in Frankfurt am Main, the magazine reports.
The scandal has caused the biggest diplomatic rift between Germany and the US in living memory, reports the BBC's Damien McGuinness in Berlin.
Mrs 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.