The Israeli military said more than 25 mortar shells have been fired from the Gaza Strip toward communities in southern Israel.
The military said most were intercepted by the Iron Dome defence system and no one was hurt in the barrage.
But the volume of mortars would appear to be the largest fired in a single incident since the 2014 Israel-Hamas war.
Israeli media reported that one of shells landed near a kindergarten shortly before it opened.
The border area has been tense in recent weeks as the Palestinians have held mass protests aimed at lifting a blockade imposed by Israel and Egypt after Hamas seized power in 2007.
Israeli fire has killed more than 110 Palestinians, most of them during the Hamas-led protests, which climaxed on May 14.
On Sunday, Israeli shelling killed three Palestinian militants from the smaller Islamic Jihad group after the troops found a bomb planted along the border.
Islamic Jihad vowed retaliation.
On Monday, a tank fired at a Hamas position in the Gaza Strip, killing one man and wounding another, after Israeli troops came under fire on the frontier while apprehending two armed Palestinians.
Hamas has said that a boatful of students and medical patients is to set sail out of Gaza City’s port on Tuesday, aiming to break 11 years of naval blockade imposed by Israel, which could spark further conflict.
It has vowed to continue the border rallies.
Israel says it is defending its border as well as its communities nearby.
It accuses Hamas of trying to carry out attacks under the cover of protests.