Inter have won the last two Serie A titles and this season are six points clear with 11 games left to play.
Mancini, 43, announced he was planning to quit the Serie A champions in the news conference following his side's defeat by Liverpool in the last 16 of the Champions League.
He gave no reason for his decision at the time and Moratti said he still had no idea why the coach made his outburst, only to state his desire to stay the following day.
Moratti had expected to talk with his coach on Thursday but the meeting was brought forward following a day of shock and confusion within Italy's soccer fraternity.
Before the meeting, Moratti had said he was surprised by Mancini's decision.
"Of course I wasn't expecting it, and neither were those who are close to him," he said.
"There will be reasons for it. I think it's probably something he had in mind since the game in Liverpool because it's strange to come out with something like this all of a sudden."
Mancini, who has been in charge of Inter since 2004, took training as usual on Wednesday but did not talk to reporters.
Former Chelsea and Porto coach Jose Mourinho had been installed as the media's favourite to take over if Mancini stood by his initial decision.