Le Canard Enchaine had reported that the police had found the remains of seven cigarette butts in the cathedral.
Interviews carried out by detectives since last week's blaze have led to a number of confessions.
Eskenazi said it was impossible to set a log on fire with a cigarette butt and questioned how cigarette butts could have been found on the site.
The main suspects are renovators working for Le Bras Freres, a company based in eastern France which had won a contract to restore the spire.
He cited investigators as saying the fire started inside the cathedral, while the workers were only on the roof.
"There were colleagues who from time to time broke the rules and we regret it", said Marc Eskenazi, a spokesman for the scaffolding contractor.
France's government has presented a bill aimed at speeding up the reconstruction of Notre Dame Cathedral and providing transparency on how huge amounts of donation money for the restoration will be spent.
The inferno that raged through Notre Dame Cathedral for more than 12 hours destroyed its spire and its roof, but spared its twin medieval bell towers. "Nothing was ever done without the authorisation of the state", said Notre Dame spokesperson Andre Finot.
French officials have said that it is not ruling out any theories about the cause of the fire and investigations are continuing.
A massive fire had engulfed the historic cathedral in Paris last week while renovation work was under way.
Macron wants to rebuild the cathedral within five years - in time for the 2024 Olympics that Paris is hosting.
However, experts say the vast scale of the work to be done could easily take 15 years.