TEL AVIV, Israel -- Even as Israeli officials finished counting votes, Prime Minister Benjamin Netanyahu had begun making phone calls to secure his next coalition.

With the post-election pieces starting to fall into place, political shifts might force him to moderate the hawkish face that his previous government had shown the world.

Netanyahu will need to secure a majority of 61 seats in the 120-seat Parliament to stay on as prime minister. With Israel’s left- and right-wing parties in a dead split of 60-60 seats, analysts say securing a majority might be harder than he expected.

He’s already reached out to Yair Lapid, a former television presenter turned politician whose politically centrist Yesh Atid party surprised pundits by capturing 18 percent of Tuesday’s vote, becoming the second-largest party in the Parliament.

Israeli news stations reported Wednesday night that Lapid was pressuring Netanyahu to reject the ultra-Orthodox parties in favor of the centrists.

Speaking to Israel’s Army Radio on Wednesday, Lapid appeared set to join a Netanyahu-led coalition, though aides close to him said he was in a position to extract a high price for his loyalty. Given the likely makeup of Netanyahu’s coalition, he’s expected to face pressure to restart peace talks with the Palestinians and to take a less militaristic tone on Iran’s nuclear program.

In recent weeks, diplomatic pressure for a new peace initiative has increased as it appears that talks between Western nations and Iran have made headway. Lapid, meanwhile, has said repeatedly that he wouldn’t join a government that didn’t include "real, significant" peace talks with the Palestinians.

"He will be a moderating influence in the government," said American Democratic pollster Mark Mellman, a campaign strategist for Lapid.

Lapid’s election campaign focused on social justice and the rising inequalities in society. He has demanded an end to the automatic military exemption for thousands of ultra-Orthodox youths, and an end to the rising taxes on Israel’s middle class. His party included a broad range of public figures, all of them proving, for the first time, that an Israeli politician didn’t need to focus on security issues such as Iran to be electable.

Israeli diplomats have expressed hope that Lapid would be Israel’s next foreign minister. In an interview with The Jerusalem Post, he stressed the importance of a positive relationship with the U.S.

“It is hubris to give an ultimatum to the U.S.,” said Lapid, when asked how he felt about Netanyahu telling President Barack Obama to set "red lines" on Iran.

One Israeli diplomat based in Europe told McClatchy there was "excitement" that Lapid might be the next foreign minister.

"After years of embarrassing diplomatic decisions that have cost us some friends, we are hoping for someone who can show a more moderate face of Israel," the diplomat, who requested anonymity because he wasn’t authorized to give interviews, told McClatchy. "We are hoping he can push policy in the right direction and help us woo back our friends."

In Israel, how prime ministers form their coalitions is just as important as how they run their election campaigns. Past years often have seen the politicians with the most political know-how and ability to compromise emerge as prime minister ahead of those who may have gotten the most votes.