Prime Minister Benjamin Netanyahu and his former rival Benny Gantz announced last month that they would join forces to form a new government.
Israel is facing a third general election in a year after politicians failed to agree on the compositon of a new agreement before the deadline of midnight on Wednesday
It was their first round of direct talks since president Reuven Rivlin on Wednesday tasked Gantz with trying to form a government.
The prime minister has given up trying to form a governing coalition.
If Netanyahu fails to form a government, Israel is set on a path for its third election with its government in a deep-seated deadlock.
Blue and White and Likud are currently tied on seats after the country's second election in a year.