A motion to dissolve parliament is expected to be heard on Wednesday and could come into effect next week once a date for an election had been decided. Commentators speculated that the vote might come in March.
Israeli markets fell on the election news, with the shekel sliding 1.3 percent to a two-year low against the dollar.
The government will remain in power until a new one is sworn in. Without the backing of Lapid and Livni's centrists parties, it would be a minority caretaker administration mainly dealing with day-to-day business.
Relations between Netanyahu and Lapid -- a former television chat show host whose newly formed party came a surprise second in 2013 -- disintegrated over the finance minister's drive to exempt first-time home buyers from value added tax.
As with the 2013 election, campaigning for any 2015 vote is likely to be dominated by domestic issues, such as the high cost of living, rather than international affairs or the possibility of reviving defunct peace talks with the Palestinians.
Livni fell out with Netanyahu over the nation-state legislation, which won cabinet approval a week ago, but she has looked uncomfortable in the government ever since peace negotiations with the Palestinians collapsed in April.
A new mandate could give Netanyahu more leeway domestically to pursue his expansionist settlement policies on occupied land Palestinians seek for a state. It will also allow the prime minister to push ahead with the Jewish nation-state bill that he says is essential to protecting Israel's Jewish identity.
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