Three Israeli soldiers were wounded in the exchange of fire.
An Israeli tank drives along the border with the Gaza strip, on the Israel-Gaza border, May 29, 2018.
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.
No Israelis have been killed.
Tuesday's violence bore a striking resemblance to the run-up to past wars.
The armed wings of Hamas and Islamic Jihad claimed responsibility for the firing and said it was in response to Israel's killing of dozens of Palestinians since 30 March, mainly in Gaza border protests.
However, the attacks - as well as Israeli airstrikes on militant sites inside Gaza - fell silent by daybreak.
Early on Wednesday, Israel reportedly hit 25 Hamas targets on the Gaza Strip.
A Palestinian official said Egyptian mediation led to a ceasefire, but the terms of the "understanding" did not go beyond "a restoration of calm by both sides".
Brig. Gen. Ronen Manelis, the chief military spokesman, threatened tougher action and said it was up to Hamas to stop the situation from escalating. The fighting mostly fell silent by daybreak amid an unofficial Egyptian-brokered cease-fire.
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"Everything we have seen in the past 24 hours is the direct doing of Iran", Bennett said. There was no Israeli comment on the purported cease-fire plan. But the protests appear to be fuelled primarily by a desire to ease the blockade. Gaza's unemployment rate is edging toward 50 percent, and the territory suffers from chronic power outages. "Unlike Hamas, they do not have any responsibility to the civilians in Gaza", he said.
"Energy Minister Yuval Steinitz, on the other hand, said that he "[estimated] that there are indirect understandings with Hamas to end the current round of violence".
No attacks were reported two hours after the announcement of the truce. One boat turned away voluntarily, while another was stopped by Israeli officials.
The report about Israel's move was widely circulated among travel agents offering trips to the Middle East on Wednesday.
"It's been a really scary morning", said Adele Raemer of Kibbutz Nirim. Conricus said the tunnel was unusual in that it snaked under Gaza's southern border into Egypt's Sinai Peninsula and then made a U-turn back into Israel.
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.
But on Tuesday, the Palestinians came under criticism.
The United States has called for an emergency meeting of the UN Security Council to discuss the latest attacks on Israel from the Gaza Strip, the US mission to the United Nations said Tuesday.
"It is UNACCEPTABLE to indiscriminately fire at civilian communities!"
Many governments have condemned the expansion of settlements, saying the policy shows Israel lacks a genuine inclination towards peace. "We will continue to act in Israel's best interests", he said.