Weekly clashes at the Israel-Gaza border have kept tensions high for months.
Earlier this week, the Israeli army released details of a new tank designed more for use in guerrilla warfare conditions, a code for urban battles.
Yesterday's flare-up is the latest as demonstrations and clashes on the frontier since March have seen at least 149 Palestinians killed.
Israeli soldier and four Palestinians killed in Gaza Strip clashes
Israel did not confirm the deal, which was the second such ceasefire agreement in a week.
On Friday, a Palestinian sniper killed an Israeli soldier along the border - the first casualty Israel has sustained in the Strip in four years.
"Hamas leaders are forcibly leading us into a situation where we will have no choice, a situation in which we will have to embark on a painful, wide-scale military operation", he said during a visit to the city of Sderot.
Hamas said through the efforts of the United Nations and Egypt, the two sides agreed to restore calm in Gaza.
The Palestinians who attempted to cross the Gaza border returned back to the enclave, causing an IDF tank to strike the Hamas observation tower in response to the infiltration attempts.
The statement said that Palestinians would continue to defend Gaza and that: "It's also the resistance's national duty to deter the Israeli Occupation from imposing its own rules of engagement upon innocent civilians".
Three Hamas fighters were killed as Israeli forces unleashed a wave of deadly strikes across the Gaza Strip, targeting 60 sites in 3 Hamas battalion compounds, according to an Israeli military spokesperson. A fourth Palestinian was shot dead in protests near the border.
Last weekend saw the most severe exchange of fire between Israel and Palestinian militants in Gaza since a 2014 war, raising worries of another round of conflict.
They are also demanding an end to Israel's 12-year blockade of the Gaza Strip, which has gutted the coastal enclave's economy and deprived its roughly two million inhabitants of many basic commodities.
Prime Minister Benjamin Netanyahu of Israel and his defense minister, Avigdor Lieberman, arrived at military headquarters in Tel Aviv on Friday night for emergency meetings with top officials, a highly unusual event for the start of Sabbath.
In response to Israel's "massive" wave of airstrikes, activists began circulating the #StoptheWar hashtag in an effort to pressure the worldwide community to step in and stop Israel's efforts to launch yet another catastrophic assault on the "occupied, blockaded, unlivable, and exhausted Gaza Strip".
In recent days, the Israeli army has opened fire at groups launching such devices.
Lieberman has raised the threat of a large-scale operation in the Gaza Strip if Hamas does not stop the kites and balloons being launched.