Fabius told Kerry that the snooping, which targeted politicians, businessman and individuals with no public profile, was "unacceptable between friends and allies".
Kerry had earlier tried to defuse the row, assuring the US's "old ally" that Washington is reviewing its information-gathering techniques, a message that US President Barack Obama repeated in a call to French President François Hollande.
But French government spokesperson Najat Vallaud-Belkacem on Tuesday seemed to indicate that Paris does not want a confrontation.
"It is up to Foreign Minister Fabius to decide what line we take but I don't think there is any need for an escalation," she told France 2 television. "We have to have a respectful relationship between partners, between allies. Our confidence in that has been hit but it is after all a very close, individual relationship that we have."
Using material obtained by NSA whistleblower, Edward Snowden, Le Monde newspaper on Monday revealed massive interception of calls, SMS messages and keyboard strokes by the National Security Agency (NSA), which recorded more than 70 million calls in one 30-day period last year.
In further revelations on Tuesday it said that the NSA had shown particular interest in French internet provider Wanadoo and communications giant Alcatel-Mucent and had also spied on French embassies and France's delegation to the UN.
The spying had helped the US obtain a vote on the UN Security Council in favour of more sanctions against Iran over its nuclear programme, one NSA internal note boasted.
Operatives were instructed to use not just the Prism programme, which was exposed by Snowden, but also Upstream, a system that intercepts communications on undersea cables and the world wide web.
The US defends its intelligence-gathering in the name of the fight against "terrorism" but Le Monde says that the "secrets of major national firms" had been probed as well.
One document seen by the paper shows that between 8 February and 8 March the NSA collected 124.8 billion pieces of data on phone calls and 97.1 billion digital operations.
France is far from its principal target.
War zones like Afghanistan are high on the list, as are Russia and China and, as Le Monde also revealed, Mexico.
In Europe, Germany and the United Kingdom come ahead of France in the snooped-on league, with the government's agreement in the case of Britain.
European Commission Vice-President Viviane Redding dubbed the revelations a "scandal" and predicted further revelations.
European Union leaders should take measures to protect citizens' privacy at this week's summit, she said.