A top Salafist leader and two other militants were killed in overnight air strikes on Gaza, as Israel vowed on Sunday to "act aggressively" against jihadists.

In the first of two deadly strikes, which took place in the northern town of Jabaliya late on Saturday, the Israeli air force killed two Salafist militants in the second such raid targeting radical Islamists within a week.

Several hours later, Israeli warplanes targeted two militants from the armed wing of the Popular Front for the Liberation of Palestine (PFLP) in the southern city of Khan Yunis, killing one of them and critically injuring the second.

Speaking to the Israeli cabinet on Sunday morning, Prime Minister Benjamin Netanyahu said that jihadists were stepping up their attempts to harm Israelis and warned that it would not be tolerated.

"Global jihad is increasing its efforts to strike at us and we shall continue to act aggressively and forcefully in response, and also with preventive strikes," he said.

The attack late on Saturday killed Sheikh Hisham al-Saedini, 43, head of Salafist group Tawhid wal-Jihad, also known as the Mujahedeen Shura Council.

Saedini, a Palestinian with Jordanian citizenship who was also known as Abu al-Waleed al-Maqdisi, was riding a motorcycle when the strike hit, medical and security sources said.

Fellow activist Fayek Abu Jazar, 42, was also killed. A 12-year-old boy, who was nearby, was wounded.

The second strike came at dawn on Sunday. The PFLP militant killed was identified as Yasser Mohammad al-Atal, 23.

The Israeli army confirmed both strikes, saying the dawn raid had targeted "a terrorist squad in the southern Gaza Strip in its final preparations to fire rockets at Israel."

It came shortly after a rocket hit an open field in the Eshkol region of southern Israel, the military said.

Saedini was one of the top Salafist militants in Gaza and in late 2008 founded the Mujahedeen Shura Council, which has claimed a spate of rocket attacks on Israel in recent days.

Several hundred people attended his funeral in Bureij refugee camp in central Gaza, which took place in complete silence, an AFP correspondent said.

The Israeli army said it had targeted him over his group's involvement in "significant terror activity against Israeli civilians and... soldiers."

It said the group was behind an attack in late January 2009 in which an explosive device hit an army patrol along the Gaza border, killing one soldier and seriously wounding another.

It said Saedini had in recent days "been planning a complex attack to be carried out along the Sinai border, a collaboration between Gaza-based militants and Salafi operatives in Sinai."

But a spokesman for the Hamas-run interior ministry accused Israel of targeting "innocent civilians."

"As usual, the Zionist enemy is falsely accusing civilians and trying to find excuses for targeting them," Islam Shawan told AFP.

He said the attack was an attempt to make up for the Israeli defence establishment's "severe security failure" on October 6 when a drone sent by Lebanon's Hezbollah militia managed to enter Israeli air space before being shot down near the Dimona nuclear reactor.

In Gaza, a handful of small Salafist groups frequently challenge Hamas over its observance of a tacit ceasefire with Israel as well as its failure to implement Islamic law.

In April 2011, Hamas arrested Saedini after the kidnapping and murder of an Italian peace activist, but released him four months later following Jordanian intervention.

Saturday's strike was the second time in a week that Israel had targeted what it describes as "global jihad" activists.

On October 7, two Salafists were critically injured in an Israeli strike on the southern city of Rafah, one of whom later died. Another eight people were injured, among them five children.

In response, the armed wings of Hamas and Islamic Jihad unleashed a barrage of rocket fire in a rare show of force given that both groups normally observe a truce on anti-Israeli attacks.

The last time Hamas militants fired on Israel was during a flareup in June when militant groups fired more than 150 rockets, wounding five people, and Israel hit back with air strikes that killed 15 Palestinians.