The Israeli parliament, or Knesset, has until Wednesday midnight to establish a governing coalition or to be dissolved, reports Xinhua news agency.
Both Netanyahu's right-wing Likud party and Gantz's centrist Blue and White party has been unable to form a coalition.
Speaking during a conference here, Netanyahu said that Israel should hold "rapid elections for the direct election of the Prime Minister".
"This will save us many months for the new elections for the Knesset and lots of money.
"Let the people decide who will be the next Prime Minister," he said, adding that "exceptional situations require extraordinary solutions".
Netanyahu first issued this proposal in a post on his Facebook page on Saturday.
The Blue and White party dismissed the proposal, saying in a statement that the party was "engaged in efforts to avoid costly and unnecessary elections, and not with empty spin aimed at bringing back an election method that has shattered the governance and political system in this country in the past and resulted in complete failure".Israel has an electoral system with elections based on votes for parties, not for specific candidates. The party that wins the largest number of votes gets to form a government.
However, in the last two rounds of elections which held in April and September, no party gained enough votes to establish a governing coalition.
The post-election political deadlock means that if lawmakers fail to agree on a coalition government in the next three days, the Knesset will be dissolved and the country will go for its third round of elections in less than a year.
( With inputs from IANS )