The Spanish government has warned of a potential breakdown of trust with the US following reports that the National Security Agency monitored more than 60m phone calls in Spain in the space of one month.

As the White House struggled to contain a growing diplomatic crisis with its allies across the world, Madrid summoned the US ambassador to Spain to demand an explanation of the extent of US spying. The NSA is alleged to have intercepted 60.5m phone calls in Spain between 10 December 2012 and 8 January 2013.

In the latest revelations from the documents leaked by US whistleblower Edward Snowden, El Mundo newspaper published an NSA graphic, entitled "Spain – last 30 days", showing the daily flow of phone calls within Spain. On one day alone – 11 December 2012 – the NSA reportedly monitored more than 3.5m phone calls.

The outcry comes days after it emerged that the NSA spied on the phone calls of scores of allies, including the personal phone of the German chancellor, Angela Merkel.

It appears that the content of the calls was not monitored but the NSA recorded the serial and phone numbers of the handsets used, the locations, sim cards and the duration of the calls. Emails and other social media were also monitored in what human rights groups have called an extraordinary invasion of people's privacy. El Mundo said software called Boundless Informant was used to process the information.

Following the meeting between the US ambassador, James Costos, and Spanish government ministers, the foreign ministry released a statement, saying: "Spain has relayed to the United States the importance of preserving a climate of trust … and its interest in understanding the full reach of practices that, if true, would be considered inappropriate and unacceptable between allies".

Costos said Washington acknowledged "that some of our closest allies have raised concerns about the recent series of unauthorised disclosures of classified information". However, he defended the NSA, saying it had not only played a critical role in protecting the US, but had "also played an instrumental role in our co-ordination with our allies and in protecting their interests, as well."

At a press conference in Warsaw, during an official visit to Poland, the Spanish foreign minister, José Manuel García Margallo, said that if the monitoring of tens of millions of phone calls was confirmed, it could "lead to a breakdown in the traditional trust" between the two countries.

Margallo, who was kept informed on the showdown with the US ambassador in Madrid, warned that the NSA could have broken Spain's privacy laws, which prohibit the conservation of data in relation to electronic communications. It remains unclear whether the telephone of the prime minister, Mariano Rajoy, or other members of the Spanish government, were tapped.

There is a growing feeling in Spain that the government has not done enough to protect its own citizens. Since 2001, when the then Spanish prime minister, José María Aznar, opted to join the Iraq war, ignoring great public opposition, Spain has enjoyed warm relations with the US, albeit as a very junior partner. Aznar and former president George Bush met on numerous occasions and it is widely understood that they agreed to share intelligence. The US has CIA and NSA offices in Madrid and many believe that there would be little surprise within the Spanish intelligence community at the extent of US spying.

Amnesty International called on the Spanish government on Monday to "reflect on its total failure to protect its own citizens' privacy". The head of Amnesty in Spain, Esteban Beltrán, accused the government of only reacting when the full extent of US spying was revealed in the press: "It's not a question of legislation – because there are laws that protect the individual's right to privacy – it is question of the government failing in its duties in what can only be called a massive and arbitrary invasion of the rights of all those who live in Spain."

Amnesty called on the government to ensure that all surveillance had a "legitimate objective, and was carried out with the proper judicial supervision".

In a sign that the Spanish government is less troubled than its counterparts in Paris and Berlin, Rajoy last week rejected a move to get the EU's 28 member states to sign a "no-spy" deal. "We'll see once we have more information if we decide to join with what France and Germany have done," he said in Brussels on Friday. "But these aren't decisions which correspond to the European Union. They are questions related to national security and are the exclusive responsibility of member states. France and Germany have decided to do one thing and the rest of us may decide to do the same, or something else," he said.

But the latest revelations have forced Madrid to take a stronger public line against Washington, which is under intense pressure to reveal the extent to which US President Barack Obama was aware of the extent of surveillance operations targeting the leaders of allied countries.

The latest developments came as an EU parliamentary delegation began a visit Washington to discuss the scale of US spying on its allies. Claude Moraes, the British Labour MP who is leading the delegation, said the Snowden documents suggested that "the type of surveillance that is taking place by intelligence services is completely disproportionate in the important fight against terrorism and for security". The allegations resulting from Snowden's leaks need to be investigated, he said.

He said the MEPs hoped to meet with NSA director General Keith Alexander and said "emphasis has to be put on ensuring that there is a strong legal framework in place in the EU which not only protects EU citizens' fundamental right to privacy but also ensures that member states and third countries, including the US, respect this right, too".

In September, the European parliament's civil liberties committee launched a Moraes-led public inquiry into the surveillance of EU citizens revealed by Snowden. But Moraes complained that no EU member states had agreed to have their intelligence agencies appear at the public hearings. "It is absolutely necessary that EU governments respond to these requests so that we can establish facts and ensure that European citizens are fully informed," he said.

The White House has not commented on the reports in El Mundo.