Palestinian relatives of Ismail Al Baryen, 27, a farmer killed by Israeli fire, gather for his funeral in the village of Abasan, east of Khan Younis, in the southern Gaza Strip on Tuesday. (Eyad Baba/Associated Press)

An Israeli air strike hit the southern Gaza Strip on Tuesday, hours after an Israeli soldier was killed by a bomb attack on the edge of the Palestinian territory, Hamas officials said.

Tuesday's violence was the worst since a fragile ceasefire was declared more than a week ago.

The Islamic Hamas militant group, which controls Gaza, said one of its members was wounded in the air strike while riding a motorcycle in the southern town of Khan Younis.

Earlier Tuesday, an Israeli soldier was killed and three wounded after militants detonated a bomb targeting an Israeli army patrol near the Kissufim crossing in the central Gaza Strip, Israeli officials said.

Israeli soldiers then crossed the border in search of the attackers. Residents said Israeli tanks and bulldozers were levelling some farmland in the area where the bombing took place.

The death marks Israel's first fatality since Israel began a ceasefire on Jan. 17, followed by a ceasefire by Gaza militants a day later. The truce put an end to a bruising three-week offensive by Israel aimed at halting rocket fire from the Hamas-controlled coastal territory.

Although there was no claim of responsibility for the deadly bombing, Mushir al-Masri, a Hamas leader, said Israel was to blame for continuing to fire into Gaza. Al-Masri said his group had not agreed to a full ceasefire but only to a "lull" in fighting.

In reaction to the death, Israeli Defence Minister Ehud Barak called Tuesday for an urgent meeting of his top defence officers, saying Israel "cannot accept" the attack.

"We will respond, but there is no point in elaborating," Barak said in comments released by his office.

In what appeared to be an unconnected incident a short time after the Israeli death, Palestinian officials said Israeli troops along the border several kilometres away shot and killed a 27-year-old man they identified as a farmer. Two others were wounded.

The Gaza territory is home to 1.4 million people and has been ruled by the Islamic militant group Hamas since June 2007.

U.S. envoy to visit region

The Israeli offensive has killed 1,285 Palestinians, more than half of them civilians, according to records kept by the Palestinian Centre for Human Rights. Thirteen Israelis, including three civilians, were also killed during the fighting.

Egypt is trying to work toward a long-term truce to bring quiet to the region.

Israel has demanded an end to Hamas rocket attacks and guarantees that militants will be prevented from smuggling weapons into the coastal territory.

U.S. Secretary of State Hillary Clinton weighed in on the conflict in her first news conference on Tuesday, saying that Israel has the right to defend itself.

"We support Israel's right to self-defence. The [Palestinian] rocket barrages which are getting closer and closer to populated areas [in Israel] cannot go unanswered," Clinton said, according to Reuters.

Meanwhile, U.S. President Barack Obama vowed to improve dialogue with the Muslim world in an interview aired Tuesday on Arabic television.

He told Al Arabiya that when it comes to Middle East matters "all too often the United States starts by dictating."

Obama's new envoy to the Middle East, George Mitchell, arrives in the region Wednesday on an eight-day trip.

The president said he felt it important to "get engaged right away" in the Mideast and had directed Mitchell to talk to "all the major parties involved."

"What I told him is start by listening, because all too often the United States starts by dictating," Obama told the interviewer.

With files from the Associated Press