Mr Hollande called an emergency meeting and said France would “not tolerate” acts that threaten its security.
The US said it would not comment on “specific intelligence allegations”.
Ned Price, a spokesman for the US National Security Council, added that the US was “not targeting and will not target the communications of Mr Hollande”.
The NSA has previously been accused of spying on German Chancellor Angela Merkel and on Brazilian and Mexican leaders.
Politicians and other leading figures are taking turns on television to express outrage and indignation at the alleged US spying. From government, there are similar noises. The US ambassador is being summoned for explanations. Mr Hollande is to telephone Mr Obama. An intelligence chief is being despatched to Washington.
If that is the extent of it, though, it hardly amounts to a major rupture. From previous Wikileaks scoops, the French have known for years that they are spied on by the Americans. Only last month it was revealed that the Germans – acting on behalf of the NSA – were snooping after industrial secrets.
The unwritten rule in all of this is that if you are caught, expect a very public denunciation. But behind the scenes life will go on as normal. The fact is that the French and US intelligence services enjoy a degree of cooperation and interdependence that no government in Paris would ever dream of jeopardising.
French Foreign Minister Laurent Fabius has summoned US Ambassador Jane Hartley to discuss the latest claims, French officials said.
Ms Hartley is expected to visit the foreign ministry in Paris later on Wednesday.
A senior French intelligence official is meanwhile expected to visit Washington to discuss the spying claims.
Wikileaks began publishing the files on Tuesday, under the heading “Espionnage Elysee” – a reference to the French presidential palace.
It said the secret files “derive from directly targeted NSA surveillance of the communications” of the three French presidents as well as French ministers and the ambassador to the US.
The Wikileaks files have now been published by France’s Liberation newspaper and the Mediapart investigative website.
One of the files, dated 2012, is about Mr Hollande discussing Greece’s possible exit from the eurozone. Another one – from 2011 – alleges that Mr Sarkozy was determined to resume peace talks between Israel and the Palestinians, possibly without US involvement.
A file dated 2010 suggests that French officials were aware that the US was spying upon them and intended to complain about it.
According to the summary of an intercepted exchange, the French envoy to Washington and Mr Sarkozy’s diplomatic adviser discussed Mr Sarkozy’s plan to express his “frustration” over US unwillingness to sign a “bilateral intelligence co-operation agreement”.
“The main sticking point is the US desire to continue spying on France,” the intercept says.
It is unclear whether the material comes from data stolen by former NSA contractor Edward Snowden, the BBC’s security correspondent Gordon Corera says.
“Bugged”, left-leaning Liberation says bluntly, devoting its entire front page to the story. “The USA tapped Chirac, Sarkozy, Hollande”, says the centre-right Le Figaro, while the centrist Le Monde headline is: “How the NSA tapped conversations at the highest state level.”
A Liberation editorial entitled “Distrust” acknowledges that both Washington and Paris spy on allies and enemies but says the “US obsession with political commentary and ‘horizon scanning’ analysis … is a monumental waste of time andmoney.”
Le Figaroalso takes Washington to task for “obsessive US spying on France” adding that not just three presidents but ministers, high-ranking officials, MPs and diplomats may also have been spied on.
Le Monde notes that while the government has remained largely silent in the past, the latest revelation is “the last straw”. It says Paris asked Washington to stop spying in 2013 when Wikileaks revealed that the US was spying on French companies – but did not get a concrete answer.