He urged fellow right-wingers not to back a deal after ultra-nationalist Naftali Bennett said he would form a coalition with a centrist party.
Mr Netanyahu’s opponents have until Wednesday to form a government.
If they are successful, it would bring to an end the rule of the country’s longest serving prime minister.
Mr Netanyahu, who faces serious corruption charges and could go to jail, fell short of a decisive majority at a general election in March. It was the country’s fourth inconclusive vote in two years – and again he failed to secure coalition allies.
But his opponents might only be able to form a minority government, propped up by support from Arab members of parliament.
“Don’t form a left-wing government – such a government is a danger to Israel’s security and future,” the 71-year-old, who has dominated Israeli politics for a generation, said on Sunday. He did not elaborate.
Mr Netanyahu accused Mr Bennett of “misleading the public” and of carrying out “the fraud of the century” – a reference to the Yamina party leader’s previous public promises not to join forces with Yair Lapid, the centrist opposition leader.
