Bennett, the right-wing leader who was once former Prime Minister Benjamin Netanyahu’s chief of staff, has said that he would approach balloon attacks with the same seriousness as if they were rockets.
The Jerusalem Post reported that Israeli Defense Forces said it targeted Hamas infrastructure. About 20 fires broke out in southern Israel as a result of the balloon attack, the report said.
The New York Times, citing Palestinian news, reported that one of the Israeli strikes caused damage to at least one property, but there have been no confirmation of any casualties.
The paper reported that Israel had been on edge after the new government approved a "far-right Jewish march to pass through Palestinian areas of Jerusalem on Tuesday night."
Hundreds of Israeli ultranationalists, some chanting "Death to Arabs," paraded in east Jerusalem in a show of force that threatened to spark renewed violence.
The violence comes just three weeks after a cease-fire halted 11 days of fighting that marked the worst clashes between the IDF and Hamas militants since a small-scale war in 2014.
The Post reported that Hamas called for a "Day of Rage" to counter the march. Palestinians consider the march, meant to celebrate Israel’s capture of east Jerusalem in 1967, to be a provocation. Hamas called on Palestinians to "resist" the parade, a version of which helped ignite last month’s 11-day Gaza war.
Yair Lapid, the alternate prime minister who will serve as foreign minister for the first two years of the government’s term, said those shouting racist slogans were "a disgrace to the Israeli people."
"The fact that there are radicals for whom the Israeli flag represents hatred and racism is abominable and unforgivable," he said.
The Associated Press contributed to this report