There has been widespread speculation in Israel and Gaza of discussions on a wider peace agreement between the two sides, as tensions have soared in the region over the past few months.
One mortar shell exploded near a kindergarten building, a military spokesman said, causing damage to the structure.
"Israel will exact a heavy price from anyone who tries to attack it, and we view Hamas as responsible for preventing such attacks against us", Netanyahu said after conducting an emergency meeting at the Prime Minister's Office.
Michael said Hamas was in a hard position following weekly mass demonstrations at the Israel-Gaza border fence. With Hamas claiming there is a ceasefire, it looks like the strategy is working.
Whilst a senior Israeli official said Israel was not interested in war but would respond "forcefully" to any rocket fire from the Strip, the Times of Israel reported.
For several weeks, Hamas led violent protests and attacks along Israel's border with the Gaza Strip which it dubbed "The Great March of Return.".
Israeli forces killed at least 116 Palestinians and wounded thousands including women and unarmed demonstrators in the protests, drawing foreign censure of Israel's deadly tactics.
Israel unilaterally withdrew its settlements and military presence from Gaza in 2005.
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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 the protests appear to be fueled primarily by a desire to ease the blockade.
"It's been a really scary morning", said Adele Raemer of Kibbutz Nirim. Egypt has also kept its crossing into Gaza closed for much of the past 10 years. "The resistance factions will abide by it as long as the Occupation [the group's reference to Israel] does the same".
But on Tuesday, the Palestinians came under criticism.
The European Union's foreign policy chief, Federica Mogherini, called for an immediate halt to the rocket and mortar fire.
With most politicians unifying for a serious assault on Hamas if they don't stop attacking, the ball has been squarley placed back in their court. More than 800 Jews signed an online letter criticising Board of Deputies' president Jonathan Arkush and president-elect Marie van der Zyl for "failing to place any responsibility on Israel" in the aftermath of the clashes.
Diplomats said the United States is likely to use its veto to block adoption of that measure, but Kuwait is hoping to win backing from the 14 other council members to highlight Washington's isolation on the Israeli-Palestinian issue.
Hamas has vowed to continue the border rallies.