The EU has demanded that the United States explain a report in a German magazine that Washington is spying on the bloc, saying that, if true, such surveillance was shocking.
French President Francois Hollande called the alleged spying intolerable, saying it could hinder US relations with Paris and the European Union. "We want this to stop fast," he said.
Obama, on a visit to Tanzania, promised to supply all the information requested by European allies regarding the spying allegations, which he said Washington was still evaluating.
"Every intelligence service, not just ours, but every European intelligence service, every Asian intelligence service, wherever there's an intelligence service, here's one thing they're going to be doing: they're going to be trying to understand the world better and what's going on in world capitals around the world from sources that aren't available through the New York Times or NBC News," Obama said.
"If that weren't the case, then there would be no use for an intelligence service. And I guarantee you that in European capitals, there are people who are interested in - if not what I had for breakfast - at least what my talking points might be should I end up meeting with their leaders. That's how intelligence services operate."
His secretary of state, John Kerry, who is in Brunei for an Asian security conference, said the United States was not alone in using "lots of activities" to safeguard its security.
Revelations about the US surveillance programme, which was made public by fugitive former NSA contractor Edward Snowden, have raised a furore in the United States and abroad over the balance between privacy rights and national security.
The Guardian newspaper said on Sunday the United States had also spied on non-European allies, including Japan, South Korea and India - all represented at the Asian security conference.
Kerry confirmed that EU foreign policy chief Catherine Ashton had raised the issue when he met her in Brunei. He said he had yet to see details of the newspaper allegations.
"I will say that every country in the world that is engaged in international affairs and national security undertakes lots of activities to protect its national security and all kinds of information contributes to that. All I know is that it is not unusual for lots of nations," Kerry told a news conference.
Several EU policymakers said talks on a US-EU free trade deal should be frozen until Washington clarifies its activities.
European Commission President Jose Manuel Barroso has asked officials to carry out a security sweep of EU buildings, said Pia Ahrenkilde Hansen, spokeswoman for the EU's executive body.
Martin Schulz, president of the EU Parliament, told French radio the United States had crossed a line.
"I was always sure that dictatorships, some authoritarian systems, tried to listen ... but that measures like that are now practised by an ally, by a friend, that is shocking, if it is true," Schulz said in an interview with France 2.
Officials in Japan and South Korea said they were aware of the newspaper reports and had asked Washington to clarify them.
Indian External Affairs Minister Salman Khurshid, who is also in Brunei, told ANI television: "These are all areas of great strategic importance that we have to cooperate and collaborate in, in counter-terrorism measures.
"I think we (the United States and India) continue to remain in touch and cooperate and (if) there is any concern we would convey it or they would convey it to us," he added.
But some of Washington's European allies said counter-terrorism could not justify the scale of the alleged spying.
In an article that sparked EU outrage, Der Spiegel said on Saturday that the National Security Agency (NSA) bugged EU offices and gained access to EU internal computer networks.
On Sunday the German magazine reported that the U.S. agency taps half a billion phone calls, emails and text messages in Germany in a typical month, much more than any other European peer and similar to the data tapped in China or Iraq.
Hollande said he had told Foreign Minister Laurent Fabius to contact Kerry for an explanation and that Fabius would also meet the US ambassador in Paris "to make the point that we cannot tolerate this kind of behaviour between allies and friends".
The French president said France and the EU, if not all US partners, would need guarantees on the spying issue before going ahead with negotiations and dealings with the United States.
"We know there are systems that need to be monitored, notably in the battle against terrorism, but I don't think this risk exists within our embassies or the European Union," he declared.
In Berlin, German Justice Minister Sabine Leutheusser-Schnarrenberger said the spying reports recalled Cold War hostilities. "It goes beyond any imagination that our friends in the United States view the Europeans as enemies," she said.
Peer Steinbrueck, Social Democrat candidate for German chancellor, said the EU and European parliament should halt trade talks with Washington until "these activities are ruled out" in future, saying: "This creates a huge loss of trust."
The European Commission was cagy on whether the row would affect the EU-US free trade talks set to begin in Washington on July 8. Spokeswoman Hansen said: "All I can say is we are very much focused on the question of these allegations and we are looking for a clear statement from our American partners."
Kerry said his government thought China could have helped the United States arrest Snowden while he was in Hong Kong. Snowden is now holed up at an international airport in Russia, from where he has applied for asylum in Ecuador.
Russian President Vladimir Putin said Moscow would never hand Snowden over, but that if he wanted to stay in Russia he must "stop his work aimed at harming our American partners".