Tuesday's election ended in a deadlock, with Netanyahu's hard-line religious bloc of allies and the rival bloc of centrist, secular and Arab parties each with 60 seats, according to near-complete official results. Opinion polls had universally forecast a majority of seats going to the right-wing bloc.
Netanyahu's Likud-Yisrael Beitenu alliance captured just 31 seats, down from 42 in the outgoing parliament.
While Netanyahu, as head of the largest single party in parliament, is poised to remain prime minister, it appears impossible for him to cobble together a majority coalition without reaching across the aisle.
Lapid, whose Yesh Atid - or There is a Future - captured 19 seats, putting it in second place, is the most likely candidate to join him. In a gesture to Netanyahu, Lapid said there would not be a "blocking majority," in which opposition parties prevent the prime minister from forming a government. The comment virtually guarantees that Netanyahu will be prime minister, with Lapid a major partner.
Netanyahu said Wednesday that he would work to create a wide coalition stretching across the political divide.
Speaking to reporters, he said the election proved "the Israeli public wants me to continue leading the country" and put together "as broad a coalition as possible."
He said the next government would pursue three major domestic policy goals: to bring ultra-Orthodox Jewish men, who are routinely granted draft exemptions, into the military, to provide affordable housing, and to change the current fragmented multiparty system, which often gives smaller coalition partners outsize strength.
But Netanyahu only alluded to peacemaking in vague terms, saying coalition talks would focus on "security and diplomatic responsibility."
Netanyahu's comments were clearly aimed at the 49-year-old Lapid, a popular former TV talk-show host who has portrayed himself as an average Israeli and champion of a middle class struggling to make ends meet.
Though committed to pursuing peace, Lapid's campaign focused heavily on pocketbook issues, raising speculation that Lapid might abandon the peace agenda if he can extract other concessions from Netanyahu.
In an interview last week, Lapid criticized Netanyahu's handling of peace efforts, saying he was committed to restarting negotiations and would not serve as a "fig leaf" in a hard-line government.