JERUSALEM — For months, Israel has tried to quell Gaza’s border protests through force. Now Israel is taking a different approach, easing a blockade and allowing millions of dollars in aid to flow into Gaza, the impoverished enclave controlled by Hamas, its bitter foe.

The aim of the change, in a plan mediated by Egypt and with money supplied by Qatar, is to provide much-needed relief for Gaza, restore calm on the Israeli side of the border and avert another war.

The clashes along Gaza’s border have caused misery on both sides: At least 170 Palestinians have been killed, and thousands of acres of Israeli farmland have been torched.

But the change in Israel’s approach presents risks for leaders on both sides, pressures that could doom even this limited warming of relations.