It was the first time the two leaders spoke directly to each other since Netanyahu was sworn in for a third term as prime minister following Israel's general election earlier this year, Haaretz reported.
"I called to send you my blessings for Ramadan. I hope that we will have the opportunity to talk to each other, not only on holidays, and we will begin negotiations. This is important. I hope that U.S. Secretary of State John Kerry's efforts will bear fruit, " the Israeli leader said in the telephone conversation Sunday night.
Kerry met with separately with Netanyahu and Abbas during a visit in late June and said he was confident Israelis and Palestinians were on the verge of agreeing to negotiations on a lasting peace agreement.
Abbas' office released a statement concerning the weekend telephone conversation, saying the two leaders discussed Ramadan, the newspaper said.
Ramadan, considered a time of spiritual reflection, will end Aug. 7. Throughout the month, Muslims fast and pray during the day and gather for festive meals in the evening.
Kerry is expected to return to the region in the near future.