According to The Jerusalem Post, unofficial results will be available by Wednesday and the official winner will be declared on September 25.
The final opinion polls on Monday night has put Netanyahu's right-wing Likud party neck and neck with its main challenger, the centrist Blue and White party led by former military chief Benny Gantz.
Likud and Blue and White have 35 seats each in the 120-seat Knesset or Parliament.
In an appeal to the voters, Netanyahu, who has been the Prime Minister since 2009, wrote in the Maariv newspaper on Monday "We find ourselves at the high point of an historic change in the history of the Jewish people and the State of Israel.
"I am asking now for your confidence in order to complete the historic task and fortify the State of Israel's borders and security forever."
Last week, Netanyahu declared that he would "apply Israeli sovereignty" in the Jordan Valley if he won a record fifth term in office. The announcement amounted to a promise to effectively annex 30 per cent of the occupied West Bank, which Palestinians want to be part of a future state.
Netanyahu also reiterated a pledge from the last election to annex Jewish settlements in the West Bank.
Meanwhile, Gantz wrote in Maariv that a victory for Blue and White, which he founded in February along with former Finance Minister Yair Lapid, leader of the Yesh Atid party, would "change the direction of the ship of state of Israeli democracy", reports the BBC.
"No more instigating rifts in an attempt to divide and conquer, but rather quick action to form a unity government.
"No looking out for the interests of pressure groups, but rather a government that looks out for the majority of Israeli citizens," he added.