Describing himself as "the end user of this kind of intelligence," Obama said he telephones Hollande or German Chancellor Angela Merkel or British Prime Minister David Cameron if he wants to know what they're thinking.
"Ultimately, you know, we work so closely together that there is almost no information that is not shared between our various countries," Obama said.
The reports elicited particular outrage in Germany, where Der Spiegel reported that NSA spying had targeted telephone and Internet connection data in Germany more than any other European nation.
Citing the Snowden documents, the news magazine reported that an average of up to 20 million phone connections and 10 million Internet data connections are surveyed daily. Der Spiegel noted that the intensity of surveillance puts the U.S. ally on par with China, Iraq and Saudi Arabia.
Merkel's spokesman, Steffan Seibert, cautioned Monday against taking the report as fact without further confirmation.
"If it is, though, confirmed that diplomatic representations of the EU and some European countries were spied upon, we have to say clearly: The bugging of friends is unacceptable," Seibert said. "That cannot happen at all. We are no longer in the Cold War."
The German and French foreign ministries planned to meet with the U.S. ambassadors to those countries to talk about the allegations.
The Italian Foreign Ministry called the reports "a very thorny affair," while European Parliament President Martin Schulz said Sunday he was "deeply worried and shocked" by the claims.
"If the allegations prove to be true, it would be an extremely serious matter which will have a severe impact on EU-U.S. relations," he said.
Another report Sunday claimed that surveillance extended beyond European offices.
The Guardian newspaper reported that one NSA document leaked by Snowden describes 38 embassies and missions as "targets" and details surveillance methods that include planting bugs in communications equipment and collecting transmissions with specialized antennae.
Targets included France, Italy, Greece, Japan, Mexico, South Korea, India and Turkey, according to The Guardian.
CNN has not independently confirmed the allegations in the reports from Der Spiegel and The Guardian.
What the U.S. has to say
The U.S. Director of National Intelligence's office declined to comment Sunday on specific allegations published in Der Spiegel.
"The United States government will respond appropriately to the European Union through our diplomatic channels, and through the EU/U.S. experts' dialogue on intelligence that the U.S. proposed several weeks ago," the DNI office said in a statement. "We will also discuss these issues bilaterally with EU member states. While we are not going to comment publicly on specific alleged intelligence activities, as a matter of policy, we have made clear that the United States gathers foreign intelligence of the type gathered by all nations."
Ventrell referred to the DNI statement Monday, repeatedly telling reporters that the United States would deal directly with European allies on the matter instead of making public statements.
Snowden has revealed himself as the source of documents outlining a massive effort by the NSA to track cell phone calls and monitor the e-mail and Internet traffic of virtually all Americans.
Now Snowden faces espionage charges in the United States and was seeking asylum from Ecuador.
Vice President Joe Biden asked Ecuador "to please reject" the request for asylum, according to Ecuadorian President Rafael Correa.
Snowden and his asylum bid
On Saturday night, Correa said the ball was in Russia's court.
"In order to process this request, he needs to be in Ecuadorian territory," Correa said in an interview with Ecuador's Oromar TV on Saturday night. "At this point, the solution for Snowden's final destination is in the hands of the Russian authorities."