Abete was elected Monday and the meeting with Donadoni was his first official act. The new president complimented the coach for Italy's 2-0 win over Scotland last week in European Championship qualifying.
Italy is still fourth in its qualifying group, trailing leaders Scotland, France and Ukraine by two points.
Critics were calling for Donadoni to be fired before the Scotland win.
Abete was the chief of Italy's delegation when the Azzurri won their fourth World Cup title in Germany last year.
Malaysia needs Russia's assistance in maintaining and repairing Su-30MKM fighter jets
Posters for the play "Adam and Eve. Life after Paradise" with pictures of dancers Arsen Aghamalyan and Oksana Vasilyeva were banned in the city of Tver, Central Russia