The reports published in French daily Le Mondeand 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.
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 Monday 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 on Monday 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.
According to the paper, the spy agency automatically picked up communications from certain phone numbers in France and recorded certain text messages under a programme code-named "US-985D".
Le Monde said the documents gave grounds to believe that the NSA targeted not only people suspected of being involved in terrorism but also high-profile individuals in business and politics.
US authorities declined comment to the French daily on the "classified" documents.
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 on Sunday.
"This practice is unacceptable, illegitimate and contrary to Mexican law and international law."
This is not the first time that France and Mexico have been hit by allegations of spying by the NSA since information leaked by Snowden first emerged in June.
Mexico's current President Enrique Pena Nieto has already complained to his US counterpartBarack Obama over reports US spies have gone through his emails.
And Der Spiegel reported last month that in 2010 the NSA monitored the internal computer network of France's diplomats and that of the foreign ministry itself.
But France itself has also been accused of spying. Le Monde reported over the summer that intelligence services intercepted all communications in the country, stocking telephone and computer data for years — accusations denied by the government.
Snowden, who has taken refuge in Russia, is wanted in the United States for espionage and other charges after the leaks.
The fugitive went into hiding in Hong Kong in May and flew to Moscow on June 23, where he stayed in the transit area for more than a month before being given temporary asylum and leaving the airport for a safe location.
Snowden's revelations have caused Obama acute embarrassment in his relations with other allies.
He has since proposed reforms of US surveillance programmes in the wake of the furore.
France ‘shocked' over US spy claims, demands answers