A virtual meeting of the 20 top flight sides on Wednesday saw 16 of them favour June 13, with four clubs choosing the other alternative of June 20.
Like most leagues around Europe, Serie A has been suspended since March 10 because of the Coronavirus pandemic.
A statement from Serie A read: "The Assembly of Lega Serie A met today [Wednesday] with all the clubs present and connected via video conference.
"Lega Serie A reiterates, in the relationship with the licensees of the audio-visual rights 2018-2021, the need to comply with the payment deadlines set by the contracts to maintain a constructive relationship with them.
"As regards the resumption of sporting activity, the date of June 13 for the resumption of the championship was indicated, in accordance with government decisions and in accordance with the medical protocols for the protection of players and all professionals."
Players have already been cleared to begin individual training using their club’s facilities but group training will commence from Monday.
In accordance with government protocols, it has been agreed that if a player upon the resumption of the league tests positive for Covid-19, he and his teammates will go into a 14-day quarantine.
Juventus were leading Lazio by a point when the league was suspended.
The German Bundesliga will become the first major European league to resume this weekend.
