Palestinian president Mahmoud Abbas and exiled Hamas leader Khaled Meshaal held a second day of talks in Qatar on Friday, a Palestinian source told AFP.

The meeting -- hosted by Qatar's emir -- was a "follow up" to Thursday's talks, which lasted nearly three hours, the source said on condition of anonymity.

The discussions, at the palace of Qatari ruler Sheikh Tamim bin Hamad al-Thani, came after Israel's offensive on Gaza flared anew on Tuesday as Egyptian-brokered truce efforts collapsed.

They broke down with Israel insistent on its demand for security from rocket fire by Palestinian factions, and Hamas defiant over its call for an end to eight years of Israeli blockade.

In Qatar, no information was immediately available on the content of the discussions there. The Palestinian source said Abbas would leave Doha after the meeting.

The Hamas armed wing declared the truce efforts over Wednesday after Israel carried out an abortive assassination attempt on its leader Mohammed Deif, killing his wife and two of his children.

Four Palestinians were killed in new Israeli air strikes on Gaza Friday, raising the death toll since July 8 to 2,087 Palestinians dead and 67 Israelis.

The Israeli offensive on the coastal enclave is the deadliest confrontation between Tel Aviv and Hamas since the second Palestinian Intifada (uprising) between 2000 and 2005.

*This story was edited by Ahram Online.