An Israeli air strike killed a Gaza civilian and wounded 12 others, including seven children, when it hit a home next to a militant training ground, medics said on Friday.

The Israeli army expressed regret that civilians were hurt but blamed Gaza's Hamas rulers for operating within residential areas.

The overnight raid destroyed a house in eastern Gaza City, killing Bahjat al-Zaalan, 37, and injuring many of his family members, more than half of them children, emergency services spokesman Adham Abu Selmiya said.

"Seven children were wounded, two of them very seriously," he said, indicating that Zaalan's wife and daughter were also hurt in the attack as well as three other people.

The strike, which targeted a Hamas militant training ground nearby, caused the home to collapse, and several other houses nearby were also partly destroyed or burned.

The military initially issued a statement that only confirmed it carried out two raids on "terror activity sites," without mentioning the civilian casualties.

But a spokeswoman later expressed regret that civilians were hurt, while noting that "additional explosions at the sites were caused by rockets stored near the targeted terror activity sites."

"The IDF regrets that non-combatants were harmed during the course of this incident," she said, while blaming Gaza's Hamas rulers for "the placement of terror sites in a residential area."

"Ultimately it is the Hamas terror organisation that chooses to operate while embedded within a civilian population using them as a human shield to protect their activity."

The army said the strikes were in response to overnight rocket fire on southern Israel.

A police spokeswoman said five rockets had been fired across the border on Thursday, with a sixth landing on Friday morning. None of them caused damage or injury.

The rocket fire was in retaliation for a Israeli raid on Thursday afternoon which targeted a car in Gaza City, killing two militants and wounding another four people.

The military said it had targeted Issam al-Batsh, a senior member of the Al-Aqsa Martyrs Brigades, an armed off-shoot of the Fatah movement, and a second man.

It said both men had been planning an attack on southern Israel by infiltrating from the Sinai peninsula.

Batsh was also responsible for masterminding "numerous" attacks by militants who infiltrated from Sinai, including a deadly bombing in the Red Sea resort of Eilat in 2007 which killed three Israelis, the military said.

Troops along the Egyptian border have been on very high alert since the weekend over warnings of an imminent attack, fearing another incident along the lines of the one in August, when gunmen infiltrated from Sinai and shot dead eight Israelis and wounded more than 25.

Israel frequently targets militants it says are about to fire rockets over the border, or attacks Gaza in response to such rocket fire, but it also carries out targeted attacks against specific militants.