There were no reports yet of casualties.
But after Tuesday's flare-up, followed by sirens and explosions into the night, there were Palestinian claims of a ceasefire.
Earlier, IDF Spokesperson Ronen Manelis said in a press conference that the army was prepared to intensify its retaliatory raids if Hamas and Islamic Jihad continued to launch projectiles at Israel, which they have.
Israel's military had not commented, but Intelligence Minister Yisrael Katz denied talk of a deal.
"Israel takes a grave view of the attacks on it and its communities by Hamas and Islamic Jihad from the Gaza Strip", he said.
Danny Danon, Israel's permanent representative to the United Nations, blasted the proposed resolution calling it "shameful" and crafted to help Gaza's rulers Hamas.
There was no immediate claim of responsibility, but there was speculation the mortars were fired by Islamic Jihad in revenge for a recent incident that left three of its members dead.
The majority of some 28 projectiles were intercepted by Israeli air defences and no injuries were reported. One exploded in a kindergarten yard, damaging walls and scattering debris and shrapnel around the playground, about an hour before it was scheduled to open for the day. Other residents reported machine- gun fire from Gaza. U.S. Ambassador Nikki Haley said the Security Council "should be outraged and respond."
Kuwait has circulated a draft UN Security Council resolution on setting up an worldwide protection mission for Palestinians.
Prime Minister Benjamin Netanyahu vowed a forceful response after the initial mortar barrage.More news: Morocco World Cup would be 'almost European'
Israel unilaterally withdrew its settlements and military presence from Gaza in 2005. Explosions shook the Palestinian enclave and smoke rose from areas hit. It alleged some of the mortar rounds fired throughout the day were supplied by Iran.
Israel holds Hamas responsible for all violence emanating from the coastal enclave, as it has ruled Gaza since 2007.
Hamas has been severely weakened by the three wars with Israel, as well as a stifling Israeli-Egyptian blockade that has brought the local economy to a standstill.
Islamic Jihad is the second-largest armed group in Gaza after Hamas.
Hamas, the Islamist movement that runs the Gaza Strip, said in a statement "what the resistance carried out this morning comes within the framework of the natural right to defend our people".
"The Israeli occupation bears full responsibility for any upcoming escalation", it said.
Also Tuesday, two fishing boats carrying students and medical patients set sail from Gaza City's port, aiming to reach Cyprus and break the Israeli blockade, which has restricted most activity along the coast. But the protests appear to be fuelled primarily by a desire to ease the blockade.
Michael said Hamas was in a hard position following weekly mass demonstrations at the Israel-Gaza border fence.
The protests have called for Palestinians who fled or were expelled in the 1948 war surrounding Israel's creation to be allowed to return to their former homes now inside Israel. Over 110 Palestinians, many of them unarmed protesters, have been killed by Israeli fire in that time.
The high Palestinian death toll in the border protests has drawn strong global criticism of Israel, with rights groups saying Israel's use of live fire is illegal because in many cases it has struck unarmed protesters who did not pose an imminent threat to Israeli soldiers.