Prime Minister Benjamin Netanyahu has offered Yesh Atid leader Yair Lapid, Israel's newest political star, the post of foreign minister or finance minister in the new government, a newspaper reported Friday.

Yesh Atid, a centrist party formed only nine months ago, stunned the political establishment by winning 19 seats in Tuesday's Knesset election, taking second place to Netanyahu's Likud-Beitenu list suffered which a major blow, securing only 31 of the 120 seats in parliament.

The result transformed Lapid, a polished former TV anchor, author and boxer, into a kingmaker likely to play a central role in the next coalition government that Netanyahu is expected to form.

Quoting sources close to both men, who held secret talks at Netanyahu's Jerusalem home on Thursday, the top-selling Yediot Aharonot said Lapid had been offered the position as Israel's top diplomat or as head of the Treasury.

Both portfolios, as well as the defence ministry, are the most senior cabinet positions, although Lapid was not thought to be interested in taking the defence portfolio.

Israel's next finance minister will have to tackle a major budget crisis and a rash of harsh austerity cuts likely to spark widespread anger among a public already deeply unhappy over spiralling living costs.

Yediot said Lapid was more likely to be interested in the housing or interior ministries in keeping with his party's socially oriented election campaign.

Also on Thursday, Netanyahu called a raft of other party leaders, including Labour's Shelly Yachimovich whom he invited for talks on joining the government.

Although Yachimovich has vowed not to join a Netanyahu-led coalition, she accepted the invitation, Yediot said.

"It is our intention to be a strong opposition (in the face of) steps you intend to take," party sources quoted her as telling Netanyahu, in remarks reported by Haaretz.

"With regard to everything related to peace negotiations, which must be urgently resumed, the Labour party will support any such move and back it from opposition."

Yachimovich ran a campaign almost entirely devoid of reference to the Israeli-Palestinian conflict, although it is an issue the next government will have to address in light of expected renewed diplomatic pressure.