One of the dead was a local commander for Hamas's armed wing, the Ezzedine al-Qassam Brigades, a local hospital reported.
Local witnesses also said Israeli planes fired over 20 missiles into open areas in the area where the incident took place. The operation had ended and the families of the soldiers were notified, it added.
The Palestinian Health Ministry said seven people, including at least five militants, were killed and seven others were wounded. Israel's military later said the operation had ended. These are complicated operations and require a great deal of courage by the elite soldiers who sneaked into Khan Younis, and, after they were "burned", faced a long and hard path back home.
The deadly firefight in the Gaza Strip overnight does not change the fact that both Israel and Hamas are not interested in escalating tensions in the Palestinian territory, with both sides, as of Monday morning, managing to pull back from the brink of another round of violence.
Fawzi Barhoum, a spokesperson for Hamas, the Islamist movement that runs the blockaded Gaza Strip, denounced a "cowardly Israeli attack".
At least 227 Palestinians have since been killed by Israeli fire, the majority shot during protests and clashes, while others died in tank fire or air strikes.
Earlier, Netanyahu said that he was striving to reach a long-term ceasefire with Hamas rather than a new war.
Last week, Israel allowed Qatar to deliver $15m in aid to Gaza's cash-strapped Hamas rulers.
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"Several alarms have sounded in southern Israel".
Palestinian media outlets circulated photos showing the remnants of the elite Israeli military force which infiltrated into Gaza Strip Sunday night and clashed with the the Palestinian resistance. Hamas responded by lowering the intensity of the border protest last Friday.
Netanyahu had on Saturday evening defended his decision to allow Qatar to transfer the cash to Gaza, despite criticism from within his own government, saying he wanted to avoid a war if it wasn't necessary.
"Every action, without exception, has a price", he said. "And I know how to bear the price".
A total of $90 million is to be distributed in six monthly instalments, Gaza authorities said, primarily to cover salaries of officials working for Hamas.
"I'm doing what I can, in coordination with the security establishment, to return quiet to the southern communities, but also to prevent a humanitarian crisis", Netanyahu said as he readied to depart for Paris.
The payment is part of what is expected to be a set of informal understandings between Israel and Hamas reached through Egyptian and United Nations mediation.
Hamas is demanding an expansion of the permissible fishing zone off the Israeli-controlled Gaza coast, uninterrupted flow of fuel to mitigate chronic power shortages and the lifting of Israeli restrictions on exports and imports. More than 170 demonstrators, many unarmed, have been killed by Israeli army fire in the confrontations, in which numerous participants threw stones, burned tires or hurled grenades toward Israeli forces.