Five died after a missile reportedly struck a smuggling tunnel near Rafah.
The Israeli military said it had hit "terror sites and concealed rocket launchers" in response to rocket and mortar fire from the coastal territory.
Tensions have risen since a Palestinian youth was killed in apparent reprisal for the murder of three Israelis.
On Sunday, Israeli police said they had arrested six Jewish suspects in connection with the death of Mohammed Abu Khdair last week.
Hamas's military wing, the Izz al-Din al-Qassam Brigades, said Israeli aircraft had targeted a "resistance location" in the southern city of Rafah. It initially said six of its members had died, but sources later told the BBC that one man was still alive.
Medics said a smuggling tunnel near the border with Egypt had been hit by a missile, but Israeli media said there had merely been an "accident".
The Qassam Brigades also said a drone had attacked a site in northern Gaza, killing one fighter, while two other militants were killed in a separate strike east of the Bureij refugee camp in central Gaza.
The Israeli military said it had carried out strikes on at least 14 locations in retaliation for at least 39 rockets and mortars that have been fired at southern Israel since Sunday.
Lt Col Peter Lerner, an Israeli military spokesman, said the rocket fire was "unacceptable".
"We will continue to act in order to debilitate and incapacitate the Hamas terror infrastructure striking its warehouses, rocket manufacturing capabilities and those that endanger the well-being of the Israelis in the south of the country," he added.
Later, the Israeli military said a rocket had struck near the city of Beersheba, 50km (30 miles) from Gaza. An Israeli military patrol had also been attacked near the security fence along the border with Gaza, apparently with an anti-tank missile and fire-arms, it added.
Israeli Foreign Minister Avigdor Lieberman said his Yisreael Beitenu party was abandoning plans to merge with Prime Minister Benjamin Netanyahu's Likud, citing differences over how to confront Hamas and the rocket fire.
Meanwhile, Mr Netanyahu's office said that he had spoken with Mohammed Abu Khdair's father, Hussein, offering his condolences and promising to bring to justice those who killed him.
"We acted immediately to apprehend the murderers. We will bring them to trial and they will be dealt with to the fullest extent of the law," it quoted him as telling Mr Abu Khdair.
"We denounce all brutal behaviour. The murder of your son is abhorrent and cannot be countenanced by any human being," he added.
Investigators believe the 16 year old from East Jerusalem was "murdered because of his nationality", but further details have not been divulged because the case is subject to a gagging order.
His killing has triggered violent protests by Palestinians in and around Jerusalem. Dozens of people have been arrested by Israeli police.
Just hours before Mohammed Abu Khdair's death, funerals were held for the three Israeli teenagers whose bodies were found in the occupied West Bank on Monday.
The Israeli authorities have named two known Hamas operatives who they say abducted and killed Naftali Frenkel, Gilad Shaer - both 16 years old - and Eyal Yifrach, 19, last month. The group denies any involvement.
Two Palestinians armed with a gun, knives and axes stormed a synagogue complex in an ultra-Orthodox Jewish neighborhood of West Jerusalem on Tuesday morning, the Israeli police said, killing four men in the middle of their morning prayers.
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