Netanyahu's ruling right-wing Likud party took 32 seats in the Knesset (Parliament), one behind Gantz's centrist Blue and White formation, according to the almost complete vote count, meaning both fell well short of a majority, reports Efe news.
In a video message, the Prime Minister acknowledged he would be unable to form a coalition with other right-wing and ultra-Orthodox parties and called on Gantz to lend his cooperation.
"We have no choice but to form a broad unity government, as broad as possible, that is made up of all the elements that care for the State of Israel," he said.
"The nation expects us, both of us, to show responsibility and act in cooperation.
"We cannot and have no reason to go to a third election. I oppose it. A broad unity government is what is demanded of us today."
Gantz, a former Army chief, has previously said he would not join a government with Netanyahu so long as the latter, who has served as Prime Minister for a decade, was facing corruption charges.
The elections on Tuesday were slated in a bid to break the hung parliament from general elections held on April 9, when Likud and Blue and White took 35 seats each in the 120-seat Knesset.
A union of Arab parties united under the Joint List became the third force in parliament with 13 seats while the ultra-Orthodox Shas and the right-wing, secular Israel Is Our Home, led by former Defence Minister Avigdor Lieberman took nine seats each.
Israel Is Our Home looked set to be a kingmaker in the election but had refused to collaborate with Netanyahu over disagreements with ultra-Orthodox parties that traditionally work with Likud.
( With inputs from IANS )