Story highlights Der Spiegel: NSA "systematically" eavesdropped on Mexican government

It hacked into public e-mail of former president, according to the German news magazine

Mexico calls for a speedy investigation into the allegations

NSA: "The U.S. gathers foreign intelligence of the type gathered by all nations"

Unacceptable. Illegitimate. And against the law.

That's how the Mexican government responded Sunday to new allegations of U.S. spying reported by Der Spiegel.

According to the German news magazine, the National Security Agency "systematically" eavesdropped on the government. It hacked the public e-mail account of former Mexican President Felipe Calderon, which was also used by Cabinet members, Der Spiegel said.

The magazine quoted documents leaked by former NSA contractor Edward Snowden.

JUST WATCHED Risky business for whistleblowers Replay More Videos ... MUST WATCH Risky business for whistleblowers 06:14

JUST WATCHED Whistleblower: Snowden settling in well Replay More Videos ... MUST WATCH Whistleblower: Snowden settling in well 02:42

JUST WATCHED Snowden 'at peace with his decisions' Replay More Videos ... MUST WATCH Snowden 'at peace with his decisions' 05:13

"This practice is unacceptable, illegitimate and against Mexican and international law," Mexico's foreign ministry said in a statement.

It added that it would push for speedy investigation.

"In a relationship between neighbors and partners, there is no room for the practices alleged to have taken place," the ministry said.

A senior U.S. State Department official told CNN that the Mexican government reached out about the report, and that the two governments will be discussing it via diplomatic channels.

The NSA said it would not "comment publicly on every specific alleged intelligence activity, and as a matter of policy we have made clear that the United States gathers foreign intelligence of the type gathered by all nations.

"As the President said in his speech at the U.N. General Assembly, we've begun to review the way that we gather intelligence, so that we properly balance the legitimate security concerns of our citizens and allies with the privacy concerns that all people share," the agency added.

In September, Mexico and Brazil summoned U.S. ambassadors after media reports that the United States had spied on their countries' presidents.

A Brazilian news report described the alleged espionage, citing Glenn Greenwald, a Brazil-based journalist who similarly obtained documents from Snowden.

One of the alleged NSA documents leaked to Greenwald dates from June 2012, a month before Mexican President Enrique Pena Nieto was elected. In it, the candidate talks about whom he would select for his Cabinet if elected.

The documents did not reference any specific communications with Brazilian President Dilma Rousseff but show the methods the NSA allegedly used to track e-mails and mobile phone communications with close advisers.

"It was very clear in the documents that they had already carried out the spying," Greenwald told Globo TV's Sunday night program "Fantastico." "They aren't talking about something they are planning; they are celebrating their spying successes."