Police discovered two gas cylinders in the hallway of an apartment building in the French capital's western 16th district, and two others on the pavement outside, in the early hours of Saturday morning.
A mobile phone attached to the cylinders is being investigated as a possible detonator, a security source told the AFP news agency late Monday.
Speaking to Franceinfo radio on Tuesday, Interior Minister Gérard Collomb revealed that one of the arrested men was on a police terror watch list.
"That shows that the threat level in France is extremely high," added the minister, who said the incident and a knife attack in Marseille on Sunday that left two women dead underlined the importance of a tough new security law.
French lawmakers in the lower house of parliament are set to vote on Tuesday on a new counterterrorism law that rights groups and UN experts have criticised for giving too much power to police and local government officials.
In Saturday's incident in Paris, a resident alerted police after finding two gas cylinders around 4:30 am (0230 GMT) in his building in the Porte d'Auteuil neighbourhood, a source close to the probe said.
Police then found another two cylinders outside the building.
On 12 September, Collomb said that 12 planned attacks had been foiled since the beginning of the year.
Three suspected women jihadists were arrested in September last year after the discovery of gas cylinders in a car near Paris's Notre Dame Cathedral.