Explosions shook buildings throughout Gaza and rocket sirens sent Israelis in many southern towns scurrying for shelter overnight. Two Palestinians were killed and more than 100 wounded in air strikes, Palestinian officials said.
Six Israelis were wounded by a rocket, medics said.
Nine children were among the 20 dead in Gaza on Monday and scores of rockets were launched into Israel, many that were intercepted by missile defenses.
The events were unleashed by Gaza militants firing on the Jerusalem area for the first time since a 2014 war, crossing what Israeli Prime Minister Benjamin Netanyahu called a "red line."
The upsurge in violence came as Israel celebrated "Jerusalem Day," marking its capture of East Jerusalem in the 1967 Arab-Israeli war.