Israeli Defence Minister Benny Gantz said he spoke with Palestinian President Mahmoud Abbas on Monday and that the two agreed there was a need for steps to build trust.
It was the first high-level contact made public by the Israeli government, which was sworn in last month after unseating the country's longest-serving leader, Benjamin Netanyahu.
The ruling coalition is made up of left-wing, centrist, right-wing and Arab parties with little in common.
Officials have said they will focus on domestic reforms and largely avoid sweeping moves on sensitive international issues such as policy towards the Palestinians.
Mr Gantz said he shared with Mr Abbas good wishes for the Eid Al Adha holiday on Tuesday, one of the two most important festivals of the Islamic calendar.
“The discussion was positive and the two cited the need to advance trust-building steps between Israel and the Palestinian Authority, which will benefit the economy and security of the entire region,” his office said.
Mr Abbas's office confirmed the call but did not give details.
Isaac Herzog, Israel's new President, said he spoke last week with Mr Abbas who congratulated him on the new role.