In a joint statement issued after the meeting by Netanyahu's right-wing Likud and Gantz's centrist Blue and White, the parties said that the two leaders "had discussed existing political possibilities," the Xinhua news agency reported.
They agreed to meet again and to schedule more meetings of the negotiation teams of their parties.
Ahead of the meeting, Netanyahu called for "a broad national unity government," citing security issues.
"The Middle East is again in upheaval," Netanyahu told his weekly cabinet meeting, according to a statement released by his office.
"We must make tough decisions that require a government with broad shoulders," he said, referring mainly to Israel's struggle against Iran's entrenchment in Syria.
Earlier on Sunday, teams of the two parties met for negotiations. A spokesperson with Blue and White said after the meeting that Netanyahu insists on including a right-wing bloc of 55 lawmakers from pro-settler and ultra-Orthodox parties, making it impossible to form a coalition.
Both Gantz and Netanyahu said they wish to form a unity government, but they are divided over who should lead it.
Blue and White party vowed during its election campaign not to sit in government under Netanyahu, who is a suspect in at least three criminal corruption cases.
Israel's political system has been paralyzed since the closely-fought election on September 17, in which no party won enough votes to form a majority coalition in the 120-seat parliament.
The elections were the second time Israelis cast their votes in five months. Netanyahu failed to form a coalition government following the April election, which led to the second election in September.
( With inputs from IANS )