JERUSALEM — Israeli leaders have stressed two points in selling their Gaza Strip ground invasion internationally and at home: that they embraced all cease-fire proposals and that troops are targeting tunnels used by Palestinian militants to infiltrate their territory.

Now, with the lopsided death toll mounting on both sides — more than 550 Gazans, 25 Israeli soldiers and two Israeli civilians — world leaders are demanding an immediate halt to the hostilities. But the operation has uncovered more tunnels than expected, officials said, and there were two more deadly incursions Monday, making many Israelis say they were reluctant to leave a job half-finished.

That has Israel struggling with a more distilled version of the dilemma it has faced in repeated rounds against Hamas, the Islamist movement that dominates Gaza. If it stops now, it faces the prospect of a newly embittered enemy retaining the capacity to attack. But if it stays the course, it is liable to kill many more civilians and face international condemnation.