Ayalon said Israeli Prime Minister Binyamin Netanyahu should offer to recognize Palestine's statehood at the United Nations in exchange for Palestinian Authority President Mahmoud Abbas saying -- in Arabic -- he recognizes Israel's right to exist while renouncing terrorism.
The remarks came as Netanyahu seeks to form a new government after his conservative Likud party lost seats in the Knesset.
Netanyahu, if he is to form a new government, will likely have to make concessions to moderates seeking to restart the peace process.
The Jerusalem Post said a three-way summit featuring Netanyahu, Abbas and U.S. President Barack Obama -- and possibly including King Abdullah II of Jordan -- is possible this year, depending on the outcome of a meeting planned this spring between Obama and Netanyahu.
Secretary of State John Kerry is scheduled to make his first trip to Israel next week.