Israel is ramping up attacks against Iranian supply lines in Syria to block the flow of weapons to Hezbollah and other Tehran-backed militias, as it seeks to drive its foe away from its borders.

In June Israel targeted a far-flung compound near the Syria-Iraq border, according to a security official, after carrying out multiple strikes closer to home against suspected Iranian military assets in Syria, where Iran is a key backer of President Bashar al-Assad.

Israel,...