Lapid's surprise showing could make him a key Cabinet minister should he decide to join Netanyahu's government.
A Likud official said Netanyahu phoned Lapid after the results and told him, "We have the opportunity to do great things together."
Lapid and other centrist parties have said they would not join Netanyahu's team unless the prime minister promises to make a serious push for peace with the Palestinians. The moderates also want an end to the generous subsidies and military draft exemptions given to ultra-Orthodox Jewish communities.
"We have red lines. We won't cross those red lines, even if it will force us to sit in the opposition," said Yaakov Peri, a former security chief and one of Yesh Atid's leaders, told Channel 2 TV.
The conflicting positions of the various parties point up the difficulties facing anyone who tries to set up a coalition government in Israel. If Netanyahu relies only on the religious and hard-line parties, it means constant fights with the opposition over social programs. If he tries to team up with the centrists, it means battles with the ultra-Orthodox over subsidies, as well as internal sniping over concessions to the Palestinians.
Some predicted Netanyahu might even fail to form a government.
"Netanyahu's victory is a pyrrhic victory, and it is not clear he will be the next prime minister," said Israeli political analyst Yaron Ezrahi. "Netanyahu will face difficulty in constructing a viable coalition," Ezrahi said, estimating the life span of the next Israeli government at no more than 18 months.
Netanyahu has won praise at home for drawing the world's attention to Iran's suspect nuclear program and for keeping the economy on solid ground at a time of global turmoil.