The season was suspended on March 9 due to the novel coronavirus outbreak after the semi-final first legs had been played.
Sports Minister Vincenzo Spadafora confirmed on Thursday Serie A could resume on June 20 and suggested the Coppa Italia could be completed beforehand, with the second legs, Napoli v Inter Milan and Juventus v AC Milan, on June 13 and the final three days later.
"We understand the value of being able to offer all fans quality matches after months of lockdown," Scaroni told the ANSA news agency.
"But, from a sports point of view, we find it questionable to award an important trophy like the Coppa Italia with two matches in three days ... after more than three months of downtime."
The Gazzetta dello Sport said Inter Milan and Juventus were also opposed to the plans.
Two other club presidents welcomed the government's decision to restart the season.
"I'm sure that with this restart, our football will be able to maintain that high standard of quality that is recognised throughout the world," said Lazio's Claudio Lotito, whose side are second in Serie A, one point behind leaders Juventus.
Torino's Urbano Cairo said he had been sceptical about continuing the season but now agreed it should carry on.
"I was not only thinking about what is of interest to me but about a more general outlook and the health of the players and public. That's why I was doubtful," he told ANSA.
"Now, we've decided to get under way again and I'm obviously here to do things in the best possible way".
(Writing by Brian Homewood;Editing by Peter Rutherford)