He has warned previously of a long “war” against Islamist militants both at home and abroad, while Prime Minister Manuel Valls has said more attacks on French soil are inevitable.
Several summer festivals have been cancelled because they cannot meet security standards and on Friday police in Paris arrested an Afghan migrant suspected of plotting an attack on the capital, a police source said.
“Every candidate city faces the question of terrorism,” Hollande said in Friday’s edition of Le Parisien.
“No country is immune.”
Hollande arrived in Rio de Janeiro on Thursday to promote France’s bid on the eve of the opening ceremony for the 2016 games in the Brazilian city, just weeks after two deadly attacks by Islamic State loyalists in the cities of Nice and Rouen.
Hollande’s Conservative opponents have been stinging in their criticism of the president’s security track record, calling him soft on suspected militants. More than 200 people have been killed in attacks in France since January 2015.
“Indeed the threat is there, but our country is ready to face up to it. And who knows what the world will look like in 2024,” Hollande said.
France has not hosted the summer Olympics since 1924 and narrowly missed out on holding the 2012 games to London.
Traffic police in northern Paris on Friday detained an Afghan migrant a day after security services circulated his photo on suspicion he may be preparing an attack.
The city of Lille said on Friday it was cancelling the annual Lille Braderie, or flea market, because of security risks. The market dates back to the 12th century and organisers claim it is one of the largest such events in Europe.
Special security has been arranged for more than 50 such events and summer festivals this year.