Israeli media said that with 99.8 per cent of votes counted, each bloc had 60 of parliament's 120 seats.
Commentators said Netanyahu, who called early elections three months ago expecting easy victory, would be tapped to form the next government because the rival camp drew 12 of its 60 seats from Arab parties who traditionally neither are asked nor seek to join governing coalitions.
A startlingly strong showing by a political newcomer, the centrist Yesh Atid (There is a Future) party, turned pre-election forecasts on their heads and dealt Netanyahu his surprise setback in Tuesday's vote. Yesh Atid's leader, Yair Lapid, has said he would only join a government committed to sweeping economic changes and a serious push to resume peace talks with the Palestinians, which have languished throughout Netanyahu's four-year tenure.
The results were not official, and there was a slim chance of a slight shift in the final bloc breakdowns.
Addressing his supporters early Wednesday, when an earlier vote count still gave his bloc a one-seat parliamentary margin, Netanyahu vowed to form as broad a coalition as possible. He said the next government would be built on principles that include reforming the contentious system of granting draft exemptions to ultra-Orthodox Jewish men and the "responsible" pursuit of a "genuine peace" with the Palestinians. He did not elaborate, but the message seemed aimed at Lapid.
Netanyahu called Lapid early on Wednesday and offered to work together. "We have the opportunity to do great things together," Likud quoted the prime minister as saying.
The prime minister's goal of a broader coalition will not be an easy one, and will force him to make some difficult decisions. In an interview last week with The Associated Press, Lapid said he would not be a "fig leaf" for a hard-line agenda on peacemaking. A leading party member, Yaakov Peri, said Yesh Atid it would not join unless the government pledges to begin drafting the ultra-Orthodox into the military, lowers the country's high cost of living and returns to peace talks.
"We have red lines. We won't cross those red lines, even if it will cost us sitting in the opposition," Peri told Channel 2 TV.
That stance could force Netanyahu to make overtures - perhaps far more sweeping than he imagined - to get negotiations moving again.
Conversely, a coalition joining parties with dramatically divergent views on peacemaking, the economy and the military draft could easily be headed for gridlock - and perhaps a short life - at a time when Israel faces mounting international isolation, growing economic problems, and regional turbulence.
The vote tally gave Netanyahu's Likud-Yisrael Beitenu alliance 31 parliamentary seats, 11 fewer than the 42 it held in the outgoing parliament and below the forecasts of recent polls. Yesh Atid had been forecast to capture about a dozen seats but won 19.
Under Israeli law, the party with the best chance of putting together a coalition is given six weeks to do so, and Netanyahu is expected to be handed the task. In the event he fails to form a government, another party - presumably Lapid's - would be asked to try.