He and Ms. Livni, the leader of the smaller Hatnua party, described their firings as an act of cowardice.

The early elections and the heated disputes that led to the fall of the government threaten to disrupt the country yet again in a year in which it fought a 50-day war with the militant group Hamas in the Gaza Strip; in which Secretary of State John Kerry failed in his efforts to broker Israeli-Palestinian peace talks; and in which Israel has been forced to confront a new surge of deadly violence, including the murders of four Israelis in a synagogue.

Asked about the Israeli shake-up at a news conference at NATO headquarters in Brussels, Mr. Kerry said he hoped that the new elections would “produce the possibility of a government that can negotiate and move towards resolving the differences between Israelis and Palestinians, and obviously, the differences in the region.”

Israel’s march toward early elections set out last week with a row over the nationality bill. This week, it was fueled by a clash over proposed housing changes and the state budget.

Image Mr. Lapid Credit... Gali Tibbon/Agence France-Presse — Getty Images

But Israeli political analysts said the call for elections was more about Mr. Netanyahu’s need for a more malleable coalition than about disagreements over any particular issue. Mr. Netanyahu, they said, had simply had enough of his fractious coalition partners and wanted a more manageable government made up of rightist allies and the ultra-Orthodox parties he has long considered his natural partners.

“It is not about this law or that,” said Yehuda Ben Meir, a former politician and a public opinion and national security expert at the Institute for National Security Studies at Tel Aviv University. Noting that there was room for compromise on the nationality bill and that Mr. Netanyahu first voted for the housing bill, he said the prime minister appeared to have used these issues to force a coalition crisis.