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Airlines should stay away from Israel's Ben Gurion International Airport from Thursday, according to Hamas' military spokesperson.
Abu Ubaida also said the group would target Israeli public sites such as football stadiums and he cautioned Israelis living near to Gaza against returning to their homes.
Israel's prime minister has accused Hamas of using "savagery" against civilians like the Islamic State militants in Iraq.
At a news conference in Tel Aviv, Benjamin Netanyahu said there "will be a continued campaign" aimed at restoring "calm and safety" to Israeli citizens.
He added that he saw a "new diplomatic horizon" ahead for Israel in the region.
I suspect that the resumed fighting is less in Hamas' interest than in Israel's.
Hamas look weak at the minute for one thing and they barely have a friend in the world. Yes, Arab countries have condemned the Israelis over the death toll is Gaza but there have been few, if any, expressions of support for Hamas.
The same is true of the West Bank. One might have imagined that Palestinians on the West Bank would have risen up by now in support of their Gazan brethren but that hasn't been the case.
Hamas relies on global sympathy for the situation in Gaza, but of late the World's attention has been focused on the barbarism of Islamic militants in Iraq and I suspect that may have diluted any tolerance or support there was for Hamas' conduct.
They too are Islamic militants, so for the time being I think the Israeli's are going to hammer Hamas. Peace is off the table.
Israeli troops and artillery movement was filmed near the border with Gaza, as the conflict with Hamas militants continued following the breakdown of the latest ceasefire.
So far there have been no reports of direct combat although rockets have been fired into Israel, who responded with air strikes.
There have been no reported Israeli casualties while Palestinian health officials say at least 19 people have died in Israeli air strikes since the latest ceasefire ended yesterday.
An Israeli airstrike failed to kill the commander of Hamas armed wing in Gaza, according to the militant group.
In a televised statement, a masked spokesman for the Izz-el-Din al-Qassam Brigade said Israel had missed its target, Mohammed Deif.
Israeli fighter planes bombed a house in northern Gaza, killing Deif's wife, his seven-month-old son and three other people yesterday.
The spokesman said: "The leaders of the enemy were behind their offices looking at the screens and their intelligence and apparatuses made them believe that the moment of celebration was imminent. You have failed and you have missed."
He also warned of further Hamas rocket attacks on Israel's strategic interests, including Ben Gurion airport east of Tel Aviv from early on Thursday morning.
An explosion in Tel Aviv was part of a barrage of five rockets fired at Israel in the last half-an-hour, according to the country's military.
It was not immediately clear if there were any casualties. Palestinian health officials say at least 19 people have died in Israeli air strikes since the latest ceasefire ended yesterday.
An explosion has been heard in Tel Aviv, according to a tweet by the Israeli military, although it was not immediately clear what had caused it.
Israel says 175 rockets have been fired at its territory from Gaza since the latest ceasefire was broken yesterday.
There have been no reported casualties as a result of the rocket attacks.
However, Palestinian health officials say at least 19 people have died in Israeli air strikes since the ceasefire ended yesterday.
At least 19 people have died in Israeli air strikes on Gaza since the ceasefire ended yesterday, Palestinian health officials say.
Israeli aircraft have carried out 80 strikes in the Gaza Strip since Tuesday, "targeting terror sites", the military said.
A rocket fired from Gaza has hit a civilian home in Hof Ashkelon, Israel's military claims.
Israel Defence Forces also said they had targeted two Hamas fighters "responsible for rocket attacks against Israel this morning".
Latest ITV News reports
There have been two days of quiet in Gaza. No rockets or missiles, no more destroyed houses, no more ambulance sirens screaming.
A three-year-old girl has been rescued from Gaza and brought to London for life-saving heart surgery.