The premier told his Palestinian counterpart that the people of Israel seek peace and that the government would continue to work toward maintaining regional stability.
The conversation was the first between the two leaders since last year.
Eid al-Fitr is Arabic for "festival of breaking of the fast" of Ramadan, the holiest month in the Muslim calendar.
Netanyahu's phone call comes on the heels of speculation in the Israeli press that the premier has engaged the Palestinian leader in secret talks in a bid to dissuade Ramallah from pursuing actions against Israel in various international forums, including the International Criminal Court.

Benjamin Netanyahu called Mahmoud Abbas for the first time in two years to mark Eid al-Fitr. (Blaze.com)