Israel's new parliament has been sworn in, as opposition leader Gadi Eisenkot seeks to oust caretaker Prime Minister Benjamin Netanyahu.

The former army chief has been tasked with forming a government after receiving more recommendations from members of the Knesset than Netanyahu, although not all those backing him are willing to govern together.

Eisenkot's bloc of four parties won 48 seats in October's election, while Netanyahu's bloc won 53, leaving both short of a majority in the 120-seat Knesset. He has 28 days to build a coalition, with a possible two-week extension.

Almost half of the new MKs did not serve in the previous parliament, while Arab-led parties have a record number of seats.

Shortly after they were sworn in, Netanyahu and Eisenkot warned parliament about the perils of supporting a government led by the other.

"[And] to those who are thinking of establishing a government that includes supporters of terror and haters of Israel, or that will be dependent on them, I ask you, are you prepared to be dependent on those whose goal is the destruction of the Jewish state?" said Netanyahu, alluding to the prospect of an Eisenkot-led government reliant on support from Arab parties.

He also appealed for the formation of a government of national unity as the only way to confront what he said was the threat of "a nuclear Iran".

Eisenkot sharply criticised Netanyahu's comments.