According to the statement, the Palestinian "resistance" managed to "defeat" the IDF elite unit that was operating in Khan Yunis, south of the Gaza Strip, and forced the soldiers to retreat in a humiliating way.
Hamas's armed wing, the Ezzedine Al-Qassam Brigades, said the Israeli special forces team had infiltrated near Khan Yunis in the southern Gaza Strip in a civilian auto.
Israeli Prime Minister Benjamin Netanyahu told reporters Sunday that the money was "the right step" at the moment, and that he was committed to restoring quiet along the Israel-Gaza frontier and preventing a humanitarian crisis in the coastal Palestinian territory.
Palestinian militants bombarded Israel with dozens of rockets and mortar shells Monday, while Israeli warplanes struck targets throughout the Gaza Strip in what appeared to be the most intense exchange of fire since a 2014 war.
Palestinian militants launched hundreds of rockets towards Israel and Israeli jets carried out bombing raids.
The rocket attacks triggered sirens in Israeli communities close to the Gaza Strip, in the cities of Beersheba and Ashkelon, and even as far away as the Dead Sea and the West Bank's Hebron Hills. Israeli TV showed images of a building on fire in a shopping centre in the southern town of Sderot.
Israel hasn't consistently determined the perimeter of this access-restricted area along the fence with Gaza, and it has often employed deadly violence to ward off Gaza residents. The strikes have led to the deaths of at least two Palestinians. The Israeli military chief, Lt. Gen. Gadi Eisenkot, said a "special force" carried out "a very meaningful operation to Israel's security", without elaborating.
Asked Monday about the frequency of cross-border incursions into Gaza in recent years, an IDF spokesperson would only say that the army "does not discuss such matters". Egypt, Qatar and the United Nations have been working to broker a long-term ceasefire.
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Late on Sunday, Palestinians fired 17 rockets into southern Israel in response to the Israeli incursion and air strikes, which Hamas said were meant to cover the retreat of a auto used by the Israeli troops.
Hamas called the operation an "assassination of a senior leader".
A 19-year-old man was critically wounded in one explosion in southern Israel, Israeli medics said. Six others were injured.
The office of the UN's Mideast envoy, Nickolay Mladenov, said on Monday that efforts were underway "to ensure that Gaza steps back from the brink".
Earlier Monday, thousands of Palestinian mourners buried the seven militants killed in Sunday's incursion.
Hamas also canceled a weekly beach protest in northwestern Gaza along the border with Israel.
Recent weeks have seen Israel allow Qatar to provide the Gaza Strip with millions of dollars in aid for salaries as well as fuel to help ease an electricity crisis. The Israeli Ministry of Foreign Affairs shared a screenshot of the alerts, accusing Hamas of "directly & intentionally" targeting civilians. In a tweet after his arrival, he praised the slain officer.