Israel airstrikes have destroyed two Gaza City high-rises, collapsing one building and severely damaging the other, in a further escalation of seven weeks of cross-border fighting with Hamas.

Tuesday's strikes leveled the 15-story Basha Tower and severely damaged the Italian Complex, which had dozens of shops and offices.

Palestinian health officials said twenty people were wounded in the attack on the Italian Complex, which was home to seventy Gazan families.

Al Jazeera's Jane Ferguson, reporting from Gaza, said Israel fired three non-explosive warning missiles before the air strikes.

"The 13-storey [Italian Complex] building, contained 11 floors of residential units and two floors of commercial offices and a coffee shop. those floors also host the offices of the Ministry of Public Works and offices belonging to the political wing of Hamas movement," Ferguson said.

"There were some hamas offices in the building, which may be a clue as why it was targeted," she added.

Declining to comment specifically on the attacks, the Israeli military said it had hit 15 "terror sites", including some in buildings that housed Hamas command and control centres.

Since Saturday, Israel has toppled or destroyed five towers and shopping complexes in an apparent new tactic aimed at increasing pressure on Hamas.

The objects of the latest strikes contain apartments inhabited almost exclusively by middle-class Gazans, who up until now have been largely spared the considerable dislocation that has affected tens of thousands of other residents.

Since a truce between Israel and armed factions in Gaza collapsed, the death toll in the Palestinian enclave has steadily risen, with 13 more Palestinians killed in Israeli strikes since Sunday night.

On Monday, a 17-year-old boy was killed and about 25 people were wounded in a strike on a Gaza City mosque.

The Gaza religious affairs ministry said Israeli fire during the day destroyed four more mosques, raising to 71 the number of mosques destroyed over the past seven weeks.

Abdullah Mortaja, 27, a freelance journalist who previously worked for Hamas's Al-Aqsa TV, was among the latest casualties. Medical officials said he was hit by tank fire in the war-battered Shejaiya area of eastern Gaza City.

Two people wounded previously died of their injuries on Monday, raising the Gaza death toll since the July 8 start of the campaign to 2,135 with 10,915 wounded, according to the emergency services.

On the Israeli side, 68 people have been killed, the vast majority were soldiers.

Trading blame

Despite the raging violence, there were signs the sides might be edging towards a new ceasefire.

Qais Abu Leila, a senior Palestinian official involved in Egyptian-mediated talks to reach a truce, said Cairo had proposed an indefinite ceasefire.

Cairo's latest initiative calls for the immediate opening of Gaza's crossings with Israel and Egypt to aid reconstruction efforts in the coastal strip, to be followed by talks on a longer-term easing of the blockade.

Hamas and Israel blamed each other for delaying an agreement.

An Israeli official speaking on condition of anonymity told the Reuters news agency that Israel would consider the proposal if Hamas were to accept it.

Hamas spokesman Sami Abu Zuhri said of Egypt's proposals that "if Israel agreed to it, we would be heading towards an agreement".

Hamas has said it will not stop fighting until the Israeli-Egyptian blockade on the enclave of 1.8 million people is lifted.