Israel said the air strikes against Gaza are in response to rocket attacks.
The Palestinian Islamist movement Hamas has promised that Israel will "pay a tremendous price" after eight militants were killed overnight in Gaza.
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.
'UNACCEPTABLE ROCKET FIRE'
Hamas's military wing, the Izzedine 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.
Medical staff said a smuggling tunnel near the border with Egypt had been hit by a missile.
But some Israeli media quoted defence officials as saying the tunnel might have collapsed as a result of the militants' explosives detonating accidentally.
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 58 rockets and mortars that had 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," he said.
He added that strikes would continue on "warehouses, rocket manufacturing capabilities and those that endanger the well-being of the Israelis in the south of the country".
Later, the Israeli military said another three concealed rocket launchers in northern Gaza had been targeted.
It came after a rocket struck near the southern Israeli city of Beersheba on Monday morning and an Israeli military patrol came under attack near the security fence along the border with Gaza.
Prime Minister Benjamin Netanyahu's response to rocket fire from Gaza has been criticised as too weak by his foreign minister, Avigdor Lieberman. On Monday Lieberman said his Yisrael Beitenu party was scrapping a 20-month alliance with Netanyahu's Likud party as a result.
Israel has deployed more forces along the Gaza border as rocket strikes continue
Meanwhile, 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 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.