As soldiers demolished the family home of one of the two Hamas bombers, a senior government source said that its battle against the Islamist group and its leadership would not be constrained by geographical borders.

The source said that Tuesday's bombings, which left 16 people dead as well as the two bombers in the southern desert city of Beersheva, bore the fingerprints of Hamas' Damascus-based leaders.

"There will be a continuation of our targeted operations against the heads of Hamas," the source told AFP on condition of anonymity.

"There will be no geographical barrier in pursuing the terrorists and their leadership. Any place they are, there will be no immunity.

"It's Damascus that's calling the shots, the orders are coming from there."

The attacks in Beersheva were the deadliest since a suicide bombing in a restaurant in the northern port city of Haifa last October, which left 21 people and the female bomber dead.

Israel responded to that attack, carried out by smaller Islamic Jihad organisation, with an air strike on an alleged Palestinian militant training camp deep inside Syria.

Hamas has said that the Beersheva bombings, carried out by two members of its armed wing from the southern West Bank city of Hebron, were in response to the assassination of two of its leaders earlier this year.

Israeli officials were quick to argue that the Beersheva attacks were launched from an area of the West Bank which is not currently cut off from Israel by the controversial barrier.

Work on the barrier, which is eventually expected to stretch across the territory, has so far been concentrated in the north of the West Bank.

"If there was a fence in that area it would have been much harder to get into Beersheva from Hebron," Prime Minister Ariel Sharon's chief spokesman, Ranaan Gissin, told AFP.

"Now we will expedite and speed up the building of the fence there (in the south of the West Bank)," Ranaan Gissin told AFP.

"We will build the fence where it provides the best protection, not where the world decides."