Benjamin Netanyahu will return as prime minister, heading a coalition that includes parties that support Jewish settlements on Palestinian land.
Settlement supporters have secured the defence and housing ministries.
But ultra-Orthodox Jewish factions have been excluded from government for the first time in a decade.
The swearing in began after Israel’s parliament voted to approve the new government, after national elections in January gave no party a clear majority.
Speaking to parliament Benjamin Netanyahu repeated a pledge to make “a historic compromise” in order to make people with the Palestinians.
“With a Palestinian partner who is willing to conduct negotiations in good faith, Israel will be prepared for a historic compromise that will end the conflict with the Palestinians forever,” he said.
The coalition includes Benjamin Netanyahu’s Likud-Beitnu bloc, the centrist Yesh Atid party and the right-wing Jewish Home party.
The new line-up includes a strong showing of pro-settlement ministers.
Both the defence and housing ministries, which must approve construction in the occupied territories, have gone to pro-settlement activists.
The new defence minister, Moshe Yaalon, a member of Netanyahu’s Likud party, opposes any curbs on settlement-building.The new housing minister, Uri Ariel, is a Jewish settler and member of Jewish Home.
He said on Sunday the new cabinet would continue to expand settlements “more or less as it has done previously”.
This could hamper any efforts to revive peace talks with the Palestinians, which have failed to progress through Benjamin Netanyahu’s last four-year term.
The Palestinians are demanding a cessation of settlement construction as a precondition to return to negotiations.
Palestinians say that the settlements, illegal under international law, will deny them a viable state.
The settlement issue is expected to be high on the agenda when President Barack Obama visits Israel in two days’ time, along with Israeli concerns at Iran’s continued nuclear programme.
Iran insists its nuclear programme is peaceful while Israel and the West accuse it of trying to make nuclear weapons.
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