Yair Lapid, the celebrity journalist turned politician who shook the Israeli political landscape with an unexpectedly strong showing in Tuesday's election, was last night being intensively courted by parties on both right and left who are desperate to snare him for their camp.

Lapid, whose party came second, winning 19 of 120 parliamentary seats, was the target of competing appeals by Binyamin Netanyahu, who – although weakened – is expected to form another coalition government, and Shelly Yachimovich, who is likely to be leader of the opposition.

Lapid's pivotal role followed a poor result for Netanyahu's rightwing alliance, which secured 31 seats, down from a previous total of 42. In a blow to the incumbent prime minister, a sizeable proportion of former supporters are believed to have switched allegiance to Lapid, who entered politics only a year ago.

Netanyahu is considering complex options for the next coalition government, the inevitable outcome of Israel's electoral system of proportional representation. He telephoned Lapid shortly after exit polls accurately predicted the result of the election, telling him: "We have the opportunity to do great things together."

Further conversations between the pair took place in private, but one of the main issues for negotiation was thought to be an end to the exemption for ultra-Orthodox Jews from compulsory military service. The mantra of "sharing the burden" was central to Lapid's election campaign.

A statement from Netanyahu on Wednesday signalled a shift in his priorities, in order to tick the boxes of Lapid's political platform. "The Israeli public wants me to continue leading the country and it wants me to build a coalition that would create three major changes domestically: more equal distribution of the national burden [military service], affordable housing, and change in the system of government," he said.

During his first term, Netanyahu focused on security issues, with the Iranian nuclear programme at the top of his list of priorities.

Yachimovich, leader of the Labour party, urged Lapid to join an alternative centre-left camp, which could try to form a coalition government or be a robust opposition to another rightwing-religious government.

After congratulating Lapid on his "remarkable achievement", she told reporters: "I urge him not to join a Netanyahu-led government and not take part in the middle-class calamity which will happen the day after he is sworn in. Should he choose the other way – I'll stand by him and assist." She intended to do all in her power to "take advantage of the political possibility opened yesterday to form a coalition of moderate, social, peace advocate and centrist forces without Binyamin Netanyahu as prime minister".

If this was not possible, she would remain in opposition. "This will be a strong, aggressive and biting opposition and we'll do all we can to prevent Netanyahu from imposing the socially unbearable hell he's planning if he manages to form a government."

Support for Lapid accelerated in the final days of the election campaign, during which opinion polls are banned. The final surveys, published last Friday, forecast around 12 seats for Lapid's Yesh Atid party while advising that almost one in five voters was undecided.

As well as attracting disillusioned former Netanyahu voters, Lapid appears to have capitalised on the wave of anger felt in Israel in the past two years over the high cost of living, especially for young families.

Massive "social justice" protests swept the country 18 months ago, culminating in almost half a million people taking to the streets in September 2011.

"In the winter of 2013 the biggest protest of all was held. There were not half a million people there as there were in the summer of 2011; rather, it was millions of people," wrote Yael Paz-Melamed in Ma'ariv. "The silent majority in Israel, the people who work, pay taxes, go to the army, serve in reserve duty, and especially those who chose to live here freely – they got off of the couch, filled the ballot boxes and took back the power they deserve."

The White House said its relations with Israel would not change regardless of the result, but called for a resumption of long-stalled Israeli-Palestinian peace negotiations. Spokesman Jay Carney pushed back on the notion that Barack Obama and Netanyahu need to recalibrate their relationship. "No leader has met more often with or spent more time on the phone with President Obama than prime minister Netanyahu. That relationship is strong, and it is a relationship that allows for a free and open discussion of ideas and positions," Carney said.

One of Israel's most respected commentators, Nahum Barnea, wrote in Yedioth Ahronoth: "The lesson [of the election] must begin at the protest movement of the summer of 2011. By the time autumn arrived, the tents on the streets had been dismantled, the general sense was that the protest was dead and buried. That wasn't the case. The seeds had been sown. They were waiting for the rain in order to sprout, and the rain came … The feeling of disgust with the political game rules did not die: it only increased further. It went beyond Facebook posts and influenced not only the younger generation in the big cities, but other age groups and other sectors of the society."