JERUSALEM — Prime Minister Benjamin Netanyahu of Israel has so far survived corruption investigations and the threat of bribery charges without much damage to his standing. But his government teetered on the edge of collapse on Friday as Mr. Netanyahu’s coalition partners pressed for new elections over his handling of Gaza.

The call for new elections intensified after Mr. Netanyahu rebuffed on Friday a request by the hawkish leader of the Jewish Home party, Naftali Bennett, for the defense minister’s post, which opened this week with the resignation of the hard-liner Avigdor Lieberman. Mr. Bennett’s party had threatened to leave if he was not given the job.

Mr. Netanyahu has been working feverishly to shore up his governing coalition in the days since Mr. Lieberman quit his post over the government’s acceptance of what he viewed as a humiliating cease-fire to end a fierce bout of fighting in Gaza. Mr. Lieberman pulled his party out of the government, leaving Mr. Netanyahu’s coalition with a precarious parliamentary majority of one.

Mr. Netanyahu is also having to grapple with public fury. Protesters from Sderot, a southern stronghold of his conservative Likud party, and other border communities plagued by rocket fire from Gaza, have been burning tires and blocking main roads, seething over a truce they said resolved nothing and left them as vulnerable as before.