As the violence entered its 16th day, neither Israel or Islamist movement Hamas appeared willing to end hostilities, despite days of diplomatic efforts to coax them into a truce.
Palestinian emergency services said that at least six people were killed early Wednesday during prolonged shelling of the southern town of Khan Yunis and 20 more were wounded, most of them seriously.
Two more were killed by Israeli fire in the north of the Strip they said.
UN Secretary-General Ban Ki-moon, on a visit to Tel Aviv, appealed on Tuesday for the bitter rivals to "stop fighting" and "start talking.".
However Israel insisted it would keep up its aerial and ground assault until it smashes cross-border tunnels used by Gaza militants to attack the Jewish state.
A rocket crashed close to Tel Aviv's Ben Gurion international airport prompting the US Federal Aviation Authority to ban flights to and from Israel for at least 24 hours.
And the European Aviation Safety Agency advised all carriers to avoid Tel Aviv "until further notice".
The bans come after Malaysia Airlines flight MH17 was allegedly shot down by a missile over strife-torn eastern Ukraine, heightening sensitivity over aviation safety above warzones.
It was the first time such measures had been taken since the 1990-1991 Gulf war.
Israeli Prime Minister Benjamin Netanyahu appealed to US Secretary of State John Kerry to lift the ban.
"Netanyahu spoke this evening with ... Kerry and asked him to act to restore flights by American airline companies to Israel," sources in Netanyahu's office told AFP.
Kerry said the order would be reviewed within in a day and told Netanyahu the ban was solely due to safety concerns, State Department spokeswoman Jen Psaki said.
But US billionaire Michael Bloomberg said that he was flying to Tel Aviv by Israeli carrier El Al to show solidarity.
"The flight restrictions are a mistake that hands Hamas an undeserved victory and should be lifted immediately," the former New York mayor wrote on his official Twitter account.
- Ceasefire push -
Following top-level talks in Cairo, Ban went to Tel Aviv and appealed to both sides to lay down arms.
"Stop fighting, start talking and take on the root causes of the conflict so that we are not at the same situation in the next six months or a year."
The UN chief described Hamas rocket fire on Israel as "shocking" and said it must "stop immediately".
But he also said Israel must exercise "maximum restraint" in Gaza, and he urged it to take a hard look at some of the root causes of the conflict "so people will not feel they have to resort to violence as a means of expressing their grievances".
Meanwhile in Cairo, Kerry discussed ceasefire proposals with Egypt's President Abdel Fattah al-Sisi
The top US diplomat again placed the onus on Hamas to accept a ceasefire, backing an Egyptian truce initiative as a "framework" to end the fighting.
And a senior Palestinian official said talks were ongoing between president Mahmud Abbas and Hamas for a ceasefire.
Abbas pledged that Israel would be held accountable for Gaza deaths.
"We will pursue all those who commit crimes against our people, however long it takes," he said in televised comments ahead of an emergency meeting of the Palestinian leadership in Ramallah.
The meeting's concluding statement called for "widespread popular protest in solidarity with Gaza and the resistance."
Shortly afterwards, Israeli forces shot dead a Palestinian man in clashes at the West Bank village of Hussan, near Bethlehem, Palestinian security sources told AFP.
An Israeli army spokeswoman told AFP that he had been one of about of about 50 people throwing rocks and petrol bombs at soldiers.
"One of the protesters was apparently hit by rubber bullets and died from that," she said.
- UN school bombed -
Israeli fire on Tuesday hit a UN school sheltering the displaced for the second time in two days, said the United Nations' Palestinian refugee agency, UNRWA.
"UNRWA condemns in the strongest possible terms the shelling of one of its schools in the central area of Gaza," it said in a statement.
"The location of the school and the fact that it was housing internally displaced persons had been formally communicated to Israel on three separate occasions. We have called on the Israeli authorities to carry out an immediate and comprehensive investigation."
During the offensive, more than 100,000 Gazans have fled their homes, seeking shelter in 69 schools run by UNRWA.
Early Wednesday the Israeli military announced the deaths of two soldiers killed in the Gaza fighting the night before, bringing the Israeli toll to 29 soldiers and two civilians.
The army on Tuesday confirmed the death of a soldier who Hamas militants claimed they had kidnapped, but said his remains were unaccounted for.
Despite its rising body count, Israel said it would only halt its Gaza offensive after laying waste to a sophisticated network of tunnels used by militants for cross-border attacks.
A ceasefire "won't happen before we really finish the tunnels project," Justice Minister Tzipi Livni said.
She said Hamas's "completely unacceptable" preconditions for a truce had "no chance of being accepted by anyone".
Hamas has laid out a list of demands for halting its fire, including a lifting of Israel's eight-year blockade on Gaza, the release of dozens of prisoners, and the opening of its Rafah border crossing with Egypt.
The European Union appealed to Israel to keep its military operation in Gaza "proportionate" and for "all sides to implement in good faith an immediate ceasefire," a statement from a meeting of European foreign ministers in Brussels said.
It added that "All terrorist groups in Gaza must disarm," a comment welcomed by Israel.