Israeli air attacks are in response to the bombing of a jeep on patrol
Israel has carried out an air attack in Gaza and sent tanks into the Strip, after Palestinian militants killed an Israeli soldier.
Palestinian sources said there had been fighting near Khan Younis in southern Gaza. Israeli troops pulled back across the border several hours later.
It was the worst violence in Gaza since Israel's offensive against Hamas ended with both sides declaring ceasefires.
Israel closed the crosssings into Gaza on Tuesday, preventing access for aid.
An Israeli soldier on patrol in a vehicle was killed by an explosive device deliberately planted on Israel's side of the border near the Kissufim crossing, prompting troops to open fire into Gaza.
The explosion was reportedly filmed by the militants, as was gun fire and a grenade blast. Three soldiers were injured in the attack.
Israeli troops fired into the Gaza Strip in retaliation, as a result of which Palestinian officials said a farmer was killed.
Heavy fighting was reported in Khan Younis, south of the Kissufim crossing, and many people had fled their homes.
Palestinian sources say 20 Israeli tanks and seven army bulldozers made an incursion.
Two people were also wounded in an Israeli air strike in Khan Younis.
Hospital sources say one was a member of Hamas' Popular Resistance Committee who was on a motorbike at the time, and the other was a passer-by.
It was Israel's first air strike since the end of its offensive against Hamas. There has been Israeli artillery and naval fire against Gaza targets since the ceasefires were announced.
Later Palestinians said there had been another Israeli air attack on tunnels used to smuggle goods and weapons into Gaza from Egypt. They reported hearing a big explosion.
Israel closed border crossings into Gaza because of the attack on the patrol, Israeli officials said, stopping the flow of aid supplies to Gaza's 1.5 million residents.
Aid agencies have been struggling to meet the urgent needs of tens of thousands of displaced, homeless and injured people in Gaza.
The BBC's Aleem Maqbool in Gaza says that although the latest fighting has been much less intense than that of earlier this month, it is a reminder that until a long-term truce agreement is drawn up, those levels of violence could return.
The fresh fighting came as US President Barack Obama's Middle East envoy, George Mitchell, arrived in the region to seek a more permanent truce.
Mixed with the rubble and shrapnel on the floor is a shell collection, a pink hairbrush, belts, handbags, a fragment of cardboard printed with a Barbie and lots of school books, caked with dried blood
He was expected to hold talks with Egyptian officials, who have been mediating between Israel and Hamas, before travelling on to Jerusalem and Ramallah.
In Washington, Secretary of State Hillary Clinton said the US supported "Israel's right to self-defence".
"The rocket barrages which are getting closer and closer to populated areas (in Israel) cannot go unanswered," she said in her first news conference at the State Department.
Israel and Hamas declared separate ceasefires on 17 and 18 January, ending an Israeli offensive in which nearly 1,300 Palestinians and 10 Israeli soldiers were killed. Three Israeli civilians were killed by rocket fire from Gaza in the same period.
Israel said its objective to stop militant rocket fire into Israel had been fulfilled.
When Hamas called its ceasefire, it said Israel had one week to fully open all the crossings into Gaza, in order to end an 18-month blockade of the territory that has crippled its economy.
Israel wants guarantees that Hamas militants will not re-arm via smuggling tunnels under the border with Egypt.
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