Correspondents say there has been an increased number of Israeli air strikes
The Israeli military has stepped up its attacks on Gaza, as the offensive on Hamas enters its second week.
Israeli artillery and tanks bombarded the territory for what is thought to be the first time during the offensive, and further air strikes were launched.
Later, a column of military vehicles crossed into northern Gaza, Palestinian witnesses said.
In an earlier raid, at least 13 people were killed when a missile hit a mosque in Beit Lahiya, medical officials said.
Witnesses said more than 200 people had been inside the Ibrahim al-Maqadna mosque for evening prayers when it was struck.
Palestinian medics and Hamas officials said they believed dozens were injured. Four boys were among the dead, hospital officials told the AFP news agency.
The BBC's Katya Adler in Jerusalem says the Israeli military has destroyed a number of mosques since it began its Gaza campaign a week ago. Israel says Hamas uses them to store weapons.
The Israeli government insists its military offensive will continue until the group's infrastructure is sufficiently weakened to stop all attacks on Israeli civilians.
Palestinian militants in Gaza fired more rockets into southern Israel on Saturday, one of which hit the port of Ashdod, injuring two people.
Israel has now carried out more than 800 strikes on Gaza since launching the offensive a week ago, including 40 on Saturday.
The UN has warned of a worsening humanitarian crisis, and believes 25% of more than 400 Palestinians killed by Israel so far were civilians. Four Israelis have been killed by rocket fire from Gaza.
Plumes of black smoke rose from northern and eastern Gaza as night fell on Saturday after Israeli artillery and tanks massed near the border bombarded the coastal territory for what is thought to be the first time in the offensive.
Palestinian militants meanwhile fired more rockets into southern Israel
Israeli media said the military was targeting Hamas infrastructure, personnel and rocket-launching sites along the entire length of the frontier.
A BBC correspondent on the border says increasing numbers of aircraft had also been pounding targets in Gaza City all day.
The main road through the Gaza Strip was bombed in three different places, making travel from one side to the other almost impossible, reports say.
Another two commanders of Hamas's military wing, Abu Zakaria al-Jamal and Mohammed Maaruf, were also killed in separate Israeli air strikes. Their deaths came only two days after the death of a top military leader, Nizar Rayyan.
In another strike, at least one person was killed as large parts of the American International School in Beit Lahiya were destroyed. The Israeli military said the school had been used to launch rockets.
The Hamas government in Gaza said on Saturday that the Israeli military action would not "change realities" in the territory.
"Whoever thought a change in the political area could come through the bombs of planes and the tanks and without dialogue is an illusionist," it said in a statement.
BBC Middle East Editor Jeremy Bowen says that because a week of aerial bombardment has not been able to stop militant rocket attacks, the Israeli military now has to decide whether to send in its ground troops.
But Israel's Deputy Defence Minister, Matan Vilnai, played down speculation that Saturday's artillery fire heralded an ground offensive.
"I don't think this is the next stage. This is part of a military campaign being waged and now artillery cannons have joined in," he said.
Earlier, the exiled political leader of Hamas, Khaled Meshaal, warned a "black destiny" awaited Israel if it launched a ground war.
"We will not break, we will not surrender or give in to your conditions," he said in a speech from the Syrian capital, Damascus.
Tens of thousands of demonstrators have meanwhile been protesting worldwide against Israel's military operations in Gaza, calling for an immediate ceasefire.
Organisers of the London protest said it was "just the start of the campaign"
The biggest was in Paris where more than 20,000 people gathered.
About 10,000 people joined a rally in London, during which hundreds of shoes were thrown at the entrance to Prime Minister Gordon Brown's residence, echoing the protest of an Iraqi journalist who threw his shoes at US President George W Bush last month.
Protests also took place in Brussels, The Hague, Amsterdam, Ankara and Cyprus.
In Israel itself, tens of thousands of Israeli Arabs staged a protest against Israel's actions in the town of Sakhnin. One politician, Jamal Zahalka, said it had been the biggest demonstration by Israel's Arab minority in the past 10 years.
President Bush, however, blamed the violence firmly on Hamas.