Israel's foreign minister says that working toward a ceasefire with Hamas is a "grave mistake" and that his country should try to topple the militant Gaza rulers instead.

Avigdor Lieberman's remarks come as international mediators try to halt new fighting between Israel and Hamas that escalated dramatically last week to the most intense confrontation between the two since Israel's war in the Palestinian territory in late December 2008.

After a lull overnight, Lieberman told Israel Radio on Monday that Hamas exploits calm to build its fighting force and smuggle in weapons to use against Israel.

The military says Palestinians have fired more than 130 rockets and mortar shells into southern Israel since Thursday. Israeli reprisals have killed 19 Palestinians.

A senior member of Gaza's ruling Hamas movement on Sunday made a rare appeal to the Israeli public to halt escalating cross-border fighting, telling an Israeli radio station in fluent Hebrew that Hamas is ready to stop its rocket fire if Israel ends its attacks on Gaza.

With fighting continuing early Sunday, Hamas' deputy foreign minister, Ghazi Hamad, delivered the message to state-run Israel Radio.

"We are interested in calm but want the Israeli military to stop its operations," Hamad said.

Hamas officials say they want calm

Hamas refuses to recognize Israel, but Hamad and other leaders of the Islamic militant group learned Hebrew during stints in Israeli prisons.

Other Hamas officials said they were in touch with mediators in hopes of restoring calm.

Hamad spoke shortly after Palestinian militants in Gaza fired several mortar shells and rockets into southern Israel. There were no reports of injuries.

"If the attacks on Israeli citizens and soldiers continue, the response will be far harsher" than it has been, Israeli Prime Minister Benjamin Netanyahu told his cabinet.

The violence escalated a week ago when an Israeli airstrike killed three Hamas militants who Israel said were planning a cross-border kidnapping. On Thursday, Hamas militants fired a guided anti-tank missile at an Israeli school bus, wounding the two people on board, including a teenage boy who was critically hurt.

Attacks bring reprisals

Since Thursday, Palestinians fired more than 120 rockets and mortars into southern Israel, prompting a series of Israeli reprisals that have killed 19 Palestinians, including six civilians, and wounded 65 others.

It has been the most intense fighting between Israel and Gaza militants since a major Israeli offensive in the Palestinian territory ended in January 2009.

While neither side appears interested in all-out war, the fear is that an isolated incident could easily spark an Israeli offensive because of the combustible situation that has developed over the past month.

Mohammed Awad, Hamas' foreign minister, told the group's Al-Quds TV station that there was a "sustained effort" to halt the fighting. "I can say we were in contact with Egypt, Turkey and the United Nations," he said.

Islamic Jihad, a smaller Palestinian militant group, also called for a halt to the violence.

Israel invaded Gaza in December 2008 in an attempt to stop years of persistent rocket fire at Israeli civilians near the Palestinian territory. Some 1,400 Gazans, including hundreds of civilians, and 13 Israelis were killed in the three-week offensive.

Until the recent flareup, cross-border violence remained at a relatively low level. However, the balance of power has gradually shifted since the war.

On Thursday, Israel first used a new system designed to intercept incoming rockets. The system, Iron Dome, has now successfully shot down eight projectiles aimed at Israeli cities, the military said, though Israeli officials say it cannot provide a complete defence.

Israel says Hamas, meanwhile, has acquired deadlier weapons since the war. It says the group now has rockets capable of striking deep into Israel, anti-aircraft missiles and sophisticated anti-tank weapons like the laser-guided missile that hit the bus on Thursday.