The reports published in French daily Le Monde and German weekly Der Spiegel claim that the US National Security Agency (NSA) secretly monitored tens of millions of phone calls in France and hacked into former Mexican President Felipe Calderon's email account.
They come on top of revelations already leaked by Snowden and published in June that the US had a vast, secret programme called PRISM to monitor Internet users, which French prosecutors are already investigating.
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French Prime Minister Jean-Marc Ayrault said he was "deeply shocked" by the revelations -- the same word used by Interior Minister Manuel Valls -- and demanded an explanation from US authorities.
"It's incredible that an allied country like the United States at this point goes as far as spying on private communications that have no strategic justification, no justification on the basis of national defence," he told journalists in Copenhagen
French Foreign Minister Laurent Fabius, on a trip to Luxembourg for a meeting with his EU counterparts, said the US ambassador had been summoned to his ministry for a meeting today morning.
"These kinds of practices between partners that harm privacy are totally unacceptable. We have to rapidly make sure that they are no longer implemented in any circumstance," he told reporters.
It was the second time in less than four months that the American ambassador in Paris has been hauled in over revelations about US snooping.
The latest leak is also expected to prove embarrassing for US Secretary of State John Kerry, who was due in Paris today for talks with Arab officials.
Fabius will raise the issue with him in talks planned for Tuesday morning, a ministry spokesman said.
The NSA monitored 70.3 million phone calls in France over a 30-day period between December 10 and January 8 this year, Le Monde reported in its online version, citing documents from Snowden.
The Le Monde article followed revelations by Der Spiegel -- also based on documents provided by Snowden -- that US agents had hacked into the Mexican presidency's network, gaining access to Calderon's account.
According to the report, the NSA said this contained "diplomatic, economic and leadership communications which continue to provide insight into Mexico's political system and internal stability."
The agency reportedly said the president's office was now "a lucrative source."
Mexican authorities said they would be seeking answers from US officials "as soon as possible" following the allegations.
"The Mexican government reiterates its categorical condemnation of the violation of privacy of institutional communications and Mexican citizens," the foreign ministry said in a statement yesterday.
"This practice is unacceptable, illegitimate and contrary to Mexican law and international law.