A spokesman for Netanyahu's Likud party said in a statement after the meeting with Bennett that the Prime Minister would try to stabilize his government on Sunday at the weekly cabinet meeting.
The party stopped short of pulling out of the government, which would have triggered an immediate collapse, but there seemed to be little prospect of holding the fractious coalition together. Ministers and smaller parties are leaving Benjamin Netanyahu's coalition, threatening his future as prime minister.
Bennett had reportedly sought the job of defense minister after the incumbent, Avigdor Lieberman, resigned earlier this week, in protest over Netanyahu's Gaza policy.
"Prime Minister Netanyahu stressed that it's important to make every effort in order to preserve the right-wing government and not to repeat the historical mistake of 1992 when a right-wing government was toppled, raised the left to power and brought the Oslo disaster upon Israel".
Israel's outgoing defense minister has warned that Hamas is only growing in strength in the blockaded Gaza Strip. "A date for the elections is expected to be decided on Sunday following a meeting of the coalition party heads".
In response to the killing of seven Hamas militants, Hamas armed wing and other Gaza-based militant groups fired barrages of rockets into Israel.
They called for tougher action against Hamas which has portrayed the ceasefire and Lieberman's resignation as a victory.More news: Int'l investigation into Khashoggi murder a necessity, FM Çavuşoğlu says
But on Thursday, leaders of some of the key coalition partners said Netanyahu should dissolve the Knesset, Israel's parliament, and call for early elections.
"We are now feeding a monster" that will only grow if not stopped, he said. "When Israel wants to win, we will win".
Finance Minister Moshe Kahlon, who heads the centrist Kulanu party, has also called for a vote to be held before the scheduled date next November.
With a major domestic political battle on his hands, Netanyahu cancelled a planned two-day visit to Austria next week for a conference on anti-semitism and anti-Zionism.
"There's no obligation to go to an election in this time of security sensitivity", the official said on condition of anonymity.
Police have recommended he be charged in two separate corruption cases and the attorney general is expected to announce in the coming months whether to put him on trial.