"During the elections, I called for the establishment of a right-wing government. But unfortunately, the results of the elections show that this was not possible," Netanyahu said in a video in Hebrew he posted online.
"The people could not decide between the two blocs. Therefore, there is no choice but to establish a broad unity government, as wide as possible, which consists of all the values that the State of Israel holds dear," he said.
Netanyahu's call for Gantz to form a unity government is part of the prime minister's plan to put pressure on the Blue and White leader and make him responsible should efforts to form a new government fail.
Netanyahu added: "Yesterday, I met with my right-wing members and concluded that we were uniting as one bloc with one joint representative for (coalition) negotiations.
"Now I say to you, MK Benny Gantz: Benny, we must establish a broad unity government today. The people expect us, both of us, to show responsibility and work to cooperate.
"That's why I am calling on you - Benny, let's meet today, anytime, to advance this crucial process. We cannot and there is no reason to hold to a third election - I am against it. We are obliged to form a unity government."
At the same time, Netanyahu's camp asked Gantz's office to set up a face-to-face meeting between the two on Thursday.
Blue and White senior officials said in response that, "Blue and White is the larger party and Benny Gantz must form a broad unity government that he heads."
A senior Blue and White official said that the unity call by Netanyahu was a political exercise.
"Bibi has decided to go with third elections and is already trying to push the blame onto us. If he steps aside, there will be a unity government within a day."
President Reuven Rivlin,w hio has vowed to do everything in hsi power to prevent a third round of elections, said Thursday he welcomes Netanyahu's call for the two parties to form a unity goverment.
Under Israeli law, Rivlin - who commands wide respect in Israel in his largely ceremonial position - is the one to tap a party leader to try to form a government after the final vote tally is in.
Meanwhile, all right-wing factions signed a "technical block" document Thursday morning, stating that they will only join a government headed by Netanyahu.
Netanyahu and Gantz came face to face Thursday morning along with President Reuven Rivlin at a memorial service in Jerusalem for the late president Shimon Peres, three years after his death.
The move came shortly after the Central Election Committee announced that with 96.5 percent of the vote counted, Gantz's Blue and White party is leading Netanyahu's Likud by 33 seats to 31.
Neither bloc, however, is able to muster the 61 Mks needed to form an outright majority in the 120-member Knesset.
Netanyahu said Wednesday that he could muster a bloc of 55 MKs from the right, far-right and religious Jewish parties.