President says NSA will assess espionage allegations as France and Germany demand answers and warn of delay to trade talks

Barack Obama has sought to limit the damage from the growing transatlantic espionage row after Germany and France denounced the major snooping activities of US agencies and warned of a possible delay in the launch next week of ambitious free-trade talks between Europe and the US.

The German chancellor, Angela Merkel, and French president, François Hollande, demanded quick explanations from Washington about disclosures by the Guardian and Der Spiegel that US agencies bugged European embassies and offices. Berlin stressed there had to be mutual trust if trade talks were to go ahead in Washington on Monday.

Hollande went further, indicating the talks could be called off unless the alleged spying was stopped immediately and US guarantees were provided.

The diplomatic row came as Edward Snowden – the fugitive National Security Agency (NSA) whistleblower, who faces espionage charges in the US and is holed up in Moscow's Sheremetyevo airport – applied for asylum in Russia. Snowden used his first public statement to attack the US for revoking his passport and accused it of bullying countries that might grant him asylum.

Russia's president, Vladimir Putin, said on Monday: "If he wants to go somewhere and someone will take him, go ahead. If he wants to stay here, there is one condition – he must stop his work aimed at bringing harm to our American partners, as strange as that sounds coming from my mouth.

"Russia never gives anyone up and doesn't plan to give anyone up. And no one has ever given us anyone."

As Washington desperately sought to contain the diplomatic fallout from the bugging controversy, Obama acknowledged the damage done by the revelations and said the NSA would evaluate the claims and inform allies about the allegations.

After the Guardian's disclosure that US agencies were secretly bugging the French embassy in Washington and France's office at the UN in New York, Hollande called for an immediate halt to the alleged spying.

"We cannot accept this kind of behaviour between partners and allies," he said. "We ask that this stop immediately … There can be no negotiations or transactions in all areas until we have obtained these guarantees, for France but also for all of the European Union … We know well that there are systems that have to be checked, especially to fight terrorism, but I don't think that it is in our embassies or in the European Union that this threat exists."

Merkel delivered her severest warning yet on the NSA debacle. "We are no longer in the cold war," her spokesman, Steffen Seibert, said. "If it is confirmed that diplomatic representations of the European Union and individual European countries have been spied upon, we will clearly say that bugging friends is unacceptable."

Seibert said Berlin was keen on the trade talks with Washington, but qualified that support: "Mutual trust is necessary in order to come to an agreement."

While Obama sought to defuse the tension amid growing anger in Europe, he also said the US agencies were simply behaving in the same way as other intelligence organisations everywhere. "Not just ours, but every European intelligence service, every Asian intelligence service, wherever there's an intelligence service – here's one thing that 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," the US president said in Tanzania.

Obama sought to reassure fellow world leaders that the scale of US espionage against friendly nations did not signify a lack of trust.

The Europeans received their first opportunity to demand answers from the top level of the Obama administration about the alleged massive scale of US spying on its EU allies when Lady Ashton and John Kerry met in Brunei. On Sunday she demanded prompt US clarification over the veracity of the media reports.

Kerry, the US secretary of state, delivered a low-key response to the growing European clamour for answers, saying the NSA activities were not unusual. "Every country in the world that is engaged in international affairs of national security undertakes lots of activities to protect its national security and all kinds of information contributes to that," he said. "All I know is that is not unusual for lots of nations."

A sense of outrage gathered momentum across Europe at the reports that US agencies were bugging and tapping EU offices in Washington and New York, as well as the embassies of several EU member states. The European commission said it had ordered a security sweep of EU buildings following the bugging disclosures. José Manuel Barroso, the commission president, had "instructed the competent commission services to proceed to a comprehensive … security sweep and check," a spokeswoman said.

The push for clear answers from the Americans threatened to derail the long-awaited talks on a transatlantic pact between the US and the EU to create the world's biggest free-trade area.

"This is a topic that could affect relations between Europe and the US," said the French trade minister, Nicole Bricq. "We must absolutely re-establish confidence … it will be difficult to conduct these extremely important negotiations."

"Washington is shooting itself in the foot," said Germany's conservative Frankfurter Allgemeine newspaper.

"Declaring the EU offices to be a legitimate attack target is more than the unfriendly act of a machine that knows no bounds and may be out of the control of politics and the courts."

A front-page editorial in Le Monde charged the Americans with very bad behaviour.

Martin Schulz, the president of the European parliament, likened the NSA to the Soviet-era KGB and indirectly suggested a delay in the talks. Greens in the European parliament, as well as in France and Germany, called for the conference to be postponed pending an investigation of the allegations. They also called for the freezing of other data-sharing deals between the EU and the US, on air transport passengers and banking transactions, for example, and called for the NSA whistleblower, Edward Snowden, to be granted political asylum in Europe. French Greens asked Hollande to grant Snowden asylum in France.

Schulz said: "I feel treated as a European and a representative of a European institution like the representative of the enemy. Is this the basis for a constructive relationship on the basis of mutual trust? I think no."

"It is shocking that the United States take measures against their most important and nearest allies, comparable to measures taken in the past by the KGB, by the secret service of the Soviet Union."

While the anger is broad and growing across Europe, it is particularly intense in Germany which, according to Snowden's revelations, is by far the main target within the EU of the NSA's Prism programme sweeping up metadata en masse, capturing and storing it.

Given the high sensitivity of data-privacy issues in Germany, the scandal could test Merkel and force her on to the offensive against the Americans as she seeks to win a third term in general elections 11 weeks away.

The opposition Social Democrats in Berlin demanded action from Merkel, but left her scope to cut a deal that would allow some snooping and data exchanges. Frank-Walter Steinmeier, the Social Democrats leader in the German parliament, said the chancellor had to insist "the mania for data collection be palpably limited".

The Germans are also incensed at the British over GCHQ's Tempora programme which is gathering electronic information from across Europe.

The Germans were given their first proper opportunity to be briefed by the British on Monday afternoon, according to Der Spiegel. London has called a video conference with the Germans at the British embassy in Berlin. The Germans are sending intelligence officers, diplomats, and officials from the interior and justice ministries to take part, the news magazine reported.

Germany's federal prosecutor's office has also opened inquiries into the NSA debacle, with a view to establishing whether German laws have been breached.