Hamas traffic police were back in the streets of Gaza City Monday, with the radical Islamic movement ruling Gaza showing a presence for the first time after three weeks of deadly and destructive Israeli attacks, residents said.

Hamas further deepened its rocket attacks into southern Israel Tuesday, sending two upgraded Russian-type Grad rockets to a distance of more than 30 kilometres, police said.

The White House called on Hamas to halt rocket attacks into Israel and agree to a lasting ceasefire as the conflict in the Gaza Strip escalated on Monday.

The United States on Saturday urged restraint from Israel in its military operations in the Gaza Strip, but simultaneously offered sharp criticism of Hamas, the organization effectively governing the

Airstrikes and artillery fire by the Israel Defence Forces (IDF) directed at militants from the Palestinian Islamist movement Hamas in the Gaza Strip killed more than 120 people on Saturday and caused

Hamas met Monday with Lebanese President Michel Suleiman and Premier Fouad Seniora.

Syria-based Khaled Mashaal said he "told both Lebanese officials that the internal Palestinian situation was good and affirmed that Hamas supported Lebanese reconciliation."