Mr Ban comes with a simple message, says the BBC's Laura Trevelyan who is travelling with the UN chief: the fighting must stop, too many people have died.
In his meetings with Palestinian and Israeli leaders, as well as senior politicians in Egypt, Jordan, Syria, Lebanon and Turkey, Mr Ban has said he will be encouraging initiatives to open border crossings and provide humanitarian aid to Gaza.
But the UN chief is not scheduled to meet representatives of Hamas - which controls the Gaza Strip - and it is not clear whether he will go to Gaza itself during his week-long trip.
Mr Mubarak has already held talks with Saudi King Abdullah amid reports Cairo is putting increasing pressure on Hamas leaders to accept a truce proposal.
One idea being floated, says our correspondent, is for Turkish troops to be deployed along Egypt's border with the Gaza Strip to prevent the smuggling of weapons.
Hamas spokesman Sami Abu Zuhri has said any ceasefire agreement would have to entail a halt to Israeli attacks, a complete withdrawal of Israeli forces and the opening of border crossings to end the blockade of Gaza.
Air strikes on Gaza cause devastation
The Israeli foreign ministry has said there is no guarantee Hamas would respect any ceasefire agreement.
Analysts say Israel may be holding back from all-out urban warfare in Gaza City, where intense street fighting could cause heavy casualties on both sides, which would be politically risky less than a month before Israel holds elections.
However, Israeli media also reports a division within the government.
Defence Minister Ehud Barak is said to favour a week-long ceasefire in Gaza to allow for the delivery of much-needed supplies and to give politicians the breathing space to hammer out a long-term truce.
But Prime Minister Ehud Olmert says he wants to press on with the military campaign for however long it takes.
'Wiping out Palestinians'
Nearly 1,000 Gazans have been killed, 4,400 have been injured, and an estimated 90,000 have fled their homes since Israel's offensive on Gaza began on 27 December, according to Palestinian figures.
Thirteen Israelis have died, three of them civilians, Israel says.
It is impossible to independently confirm casualty figures as Israel has refused to allow international journalists to enter Gaza.
A UN watchdog has accused Israel of showing a "manifest disrespect" for the protection of children in Gaza.
More than 40% of those killed in Gaza were women or children, said the UN Committee on the Rights of the Child, even though Israel had signed a UN protocol condemning attacks on places where children were likely to be present.
Palestinian Authority President Mahmoud Abbas has accused Israel of trying to "wipe out" his people.
But Israeli Defence Minister Ehud Barak said the military operation would continue in order to stop Hamas rockets being fired into Israel and to prevent arms smuggling into Gaza.
Asked if Israel's war aims had been achieved, he said: "Most of them, probably not all of them."
And militants have kept up rocket attacks, firing 25 mortars and rockets into southern Israel on Tuesday, Israel's army said.
Both Hamas and Israel rejected last week's UN Security Council resolution calling for an immediate ceasefire.
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