A senior Hamas official on Sunday made a rare direct appeal to the Israeli public to halt the current round of cross-border fighting, after a weekend of deadly violence left 19 Palestinians dead.

"We are interested in calm but want the Israeli military to stop its operations," Hamas Deputy Foreign Minister Ghazi Hamad said in an interview on Israel Radio, adding that the group would cease its rocket attacks if Israel halted its military operations against Gaza militants.

Open gallery view Masked Palestinian militants from various groups, including the Islamic Hamas movement, attend a press conference in Gaza City on April 3, 2011. Credit: AP

Another Palestinian official said that militant groups in the Gaza Strip had agreed to Arab and United Nations proposals for a truce with Israel, and said they were told that Israel had also agreed in principle.

Israel had no immediate comment, but a senior official suggested a tacit deal may have been reached.

"What happens from here on is up to the other side," the Israeli official told reporters in Tel Aviv, speaking on condition of anonymity. "It seems calmer now, but it is still not clear where this is going."

"We will judge the other side over the next few days. The extent to which Hamas controls the other militant groups will affect the way we choose to act," the Israeli official added.

Nineteen Palestinian militants and civilians in Hamas Islamist ruled Gaza have been killed since Israel launched a series of air raids on Thursday after the critical wounding of a teenager by an anti-tank rocket that was fired at a school bus.

Palestinian militants fired more than 120 rockets and mortars at Israeli communities near the Gaza Strip over the course of the weekend, with tens of thousands of people spending the past few nights in reinforced rooms.

Another five mortar rounds hit the Negev on Sunday, and two rockets exploded near Ashkelon. Another rocket targeting Ashkelon was intercepted by the Iron Dome anti-missile system. No casualties were reported in any of those incidents, but electricity was temporarily cut in parts of the region.

Hamas spokesman Sami Abu Zuhri said earlier Sunday that "the Palestinian factions are not interested in escalation," and that "if the Israeli aggression stopped, it would be natural for calm to be restored."

But Prime Minister Benjamin Netanyahu vowed Sunday to respond "most harshly" if Palestinian militants continued to fire rockets and mortar shells at Israel.

"The Israel Defense Forces hit Hamas and the terrorist organization hard over the weekend," Netanyahu told ministers at the weekly cabinet meeting in Jerusalem. "If attacks against Israeli civilians and the IDF continue, the response will be most harsh."

Interior Minister Eli Yishai called on the cabinet to agree to taking "less routine and stronger" action against the Gaza Strip, to curb the onslaught of rockets.

Yishai said he was not envisioning "another Cast Lead" operation, referring to the war launched two years ago, but rather "an expanded air operation."

"A ground operation is completely useless," Yishai said. "We need to do something stronger and not stay apathetic as we have been, in order to bring calm to the area."

Debriefing the cabinet on the situation in Gaza, Defense Minister Ehud Barak called the rocket fire "statistical".

"Of the 150 flying object, none hit except the Kornet missile fired at the bus," he said. He also downplayed Hamas' military wing's voiced willingness for a truce, telling the cabinet: "Hamas' military wing doesn't want a cease-fire".

Vice Premier Silvan Shalom chastised Barak for distinguishing between the movement's political and military wings, telling him it "weakens" Israel's defense claims.

Barak defended himself as "not making distinction" but merely "explaining the situation."

"There is no distinction when it comes to responsibility [for the attacks]," he said. "It's all Hamas."

Earlier Sunday, Barak told Israel Radio that the army would be willing to accept a mutual cease-fire with Hamas if the movement stopped firing from Gaza. "If they stop firing on our communities, we will stop firing. If they stop firing in general, it will be quiet, it will be good," Barak told Israel Radio.

When asked if Israel was considering a ground offensive into the Gaza Strip to end Hamas's rule there, Barak said all options were on the table, but that it may not be necessary.

"If it will be necessary, we will act, but when it's not necessary, we don't need to," he said. "Restraint is also a form of strength."

Security sources said Saturday that as long as rocket fire continued from the Gaza Strip, Israel would continue extensive air attacks there.

Security sources also said that while the Hamas government in the Strip wants to calm the situation, the military wing continues to allow rocket fire from its own people and other factions.