File photo: Israeli Prime Minister Benjamin Netanyahu. Photograph:( Reuters )
Netanyahu, in a video message, said he preferred to form a right-wing coalition, but the results showed it was not possible.
A spokeswoman for Gantz, leader of the centrist Blue and White party, had no immediate response to the surprise offer from Netanyahu, head of the right-wing Likud party.
The change of strategy reflected Netanyahu's weakened position after he failed again in Tuesday's election, which followed an inconclusive ballot in April, to secure a parliamentary majority.
"During the election campaign, I called for the establishment of a right-wing government but to my regret, the election results show that this is impossible," Netanyahu said.
"Benny, we must set up a broad unity government, as soon as today. The nation expects us, both of us, to demonstrate responsibility and that we pursue cooperation."
On Wednesday, Gantz said he hoped for a "good, desirable unity government". But he has also ruled out forming one with a Netanyahu-led Likud, citing looming corruption charges against the prime minister. Netanyahu denies any wrongdoing.