Explosions in Rafah and Gaza City
Israeli planes have attacked more than 60 targets in Gaza as its offensive against Hamas entered its 18th day.
The strikes came as Israeli troops advanced into the suburbs of Gaza City.
The head of the Red Cross accompanied a convoy of aid into Gaza during a three-hour ceasefire, during which witnesses said there was increased shelling.
Palestinians say more than 90,000 people have left their homes to escape the bombing. Militants, however, have kept up rocket attacks on Israel.
Thirteen rocket or mortar attacks were launched from Gaza on Tuesday, Israeli police said. No-one was hurt.
Jacob Kellenberger, the president of the International Committee of the Red Cross (ICRC), was expected to go to the main Shifa hospital in Gaza City to see patients and medical teams.
He also intended to hold talks with senior Israeli and Palestinian officials.
Last week the ICRC accused Israel of failing to fulfil its duty to help wounded civilians in Gaza, and said it was a "full-blown humanitarian crisis".
About 100 lorries entered from Israel during the ceasefire
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.
"We are working towards those two goals while at the same time keeping an eye on the diplomatic initiatives," he said during a tour of an air force base.
Meanwhile, Palestinian Authority President Mahmoud Abbas accused Israel of trying to "wipe out" his people.
"This is the 18th day of the Israeli aggression against our people, which has become more ferocious each day as the number of victims rises," he said.
"Israel is keeping up this aggression to wipe out our people over there."
US Secretary of State designate Hillary Clinton said in her Senate confirmation hearing on Tuesday that the Obama administration would make "every effort" to forge Israeli-Palestinian peace.
She said that the US must support Israel's security needs while at the same time acknowledging Palestinian aspirations.
"The president-elect and I understand and are deeply sympathetic to Israel's desire to defend itself under the current conditions, and to be free of shelling by Hamas rockets," she said.
"However, we have also been reminded of the tragic humanitarian costs of conflict in the Middle East and pained by the suffering of Palestinian and Israeli civilians."
The BBC's Aleem Maqbool, on the Israeli-Gaza border, said shelling had continued, including air and land attacks, throughout the morning ceasefire, which began at 0900 (0700 GMT).
Earlier, one Israeli officer was critically wounded when a bomb exploded in a booby-trapped house, the Israeli military said.
It denied a claim by Hamas that the militant group had destroyed two Israeli tanks.
Western areas of Gaza City also came under shellfire from Israeli gunboats.
Human rights group al-Mizan in Gaza said more than 90,000 people had fled their houses during the violence.
About 31,000 of them were staying at UN-run schools in Gaza City, which are full, in Jabaliyah camp and Shati camp. The other 60,000 were staying with neighbours and relatives.
The UN secretary general, Ban Ki-moon, is due in the region on Wednesday to push for a truce.
He has implored Israel and Palestinian militants to halt the fighting in Gaza immediately.
Mr Ban said too many people had died and there had been too much civilian suffering.
"My message is simple, direct and to the point: the fighting must stop," Mr Ban told a news conference in New York ahead of his departure on Tuesday for the Middle East.
"In Gaza, the very foundation of society is being destroyed: people's homes, civic infrastructure, public health facilities and schools."
His diplomatic tour will see talks with the leaders of Egypt, Israel and Syria as well as the Palestinian president in Ramallah.
However, UN officials say he will not be meeting representatives of Hamas, and it is not clear whether he will go to Gaza itself during his week-long trip.
Also on Tuesday, the Israeli army said one of its patrols in the West Bank had come under fire from inside Jordan. No-one was hurt in the incident and the patrol returned fire.
However, the Jordanian Armed Forces General Command has denied there was any shooting from Jordan.
An army spokesman called the Israeli military report "categorically baseless."
"An investigation showed there was no shooting at the border into Israel," he said in the statement.
Both Hamas and Israel rejected last week's UN Security Council resolution calling for an immediate ceasefire.
Palestinian medical sources say 920 people have been killed in Gaza so far, of whom 292 were children and 75 were women. Israeli officials say 13 Israelis, including three civilians, have been killed.
Israel is preventing international journalists from entering Gaza, making it impossible independently to confirm casualty figures.