The meeting -- hosted by Qatar's emir -- was a "follow up" to yesterday'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 fighting in 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 Gaza militants, and Hamas defiant over its call for an end to eight years of Israeli blockade.
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 today, raising the death toll since July 8 to 2,087 Palestinians dead and 67 Israelis.
The war is the deadliest confrontation between Israel and Hamas since the second Palestinian intifada, or uprising, between 2000 and 2005.