Alan Fisher, Al Jazeera's correspondent on the Israeli-Gaza border, said that the Israeli army had confirmed it had entered Gaza and that he had witnessed the movement of tanks and armoured vehicles in the area.
Hamas had earlier vowed to defeat the Israeli army if it invaded the territory.
The Israeli cabinet said it had called up about 9,000 reservists as part of its preparations.
The gound assault came as the death toll of Palestinians climbed past 450 on Saturday as a strike on a northern Gaza town killed at least 11 people, including one child, who were praying in a mosque.
A column of tanks entered the besieged Gaza Strip though the Beit Hanoun crossing shortly after nightfall on Saturday.
Israeli artillery had started firing shells into the Gaza Strip for the first time on Saturday, ahead of the ground offensive.
Ofir Gendelman, an Israeli foreign ministry spokesman, said: "All we asking for is to create a normal life for people of Israel. We'll keep on targeting Hamas objectives until the situation on the ground there is transformed.
"They [Israeli ground forces] will be completing the mission of the air force, going for Hamas headquarters and weapons caches and giving a blow to their capability to launch attacks into Israel.
"It will take quite a number of days to get the job done."
Marwan Bishara, Al Jazeera's senior political analyst, said: "Israel can claim in various stages that it has won this or that war against Arabs but it is obvious since the invasion of Lebanon in 1982 that there is no military solution to Israel's secueity.
"It cannot bomb its way into peaceful co-existence. Israel is trying to do all it can to destroy Hamas but with more than 400 dead, there will be more than 400 more new recruits in Gaza.
"It has taken this path and will probably pay the price in the long term, short term it's the Palestinians who pay the price."
Israeli soldiers, tanks and armoured personnel carriers had been massing along Gaza's edge for days.
"If you commit the stupidity of launching a ground offensive, then a black destiny awaits you," Khaled Meshaal, the political leader of Hamas, said on Friday.
"You will soon find out that Gaza is the wrath of God."
Earlier on Saturday, the funeral of Abu Zakaria al-Jamal, a field commander of the armed wing of Hamas, took place.
Al-Jamal, who was a senior figure in the Izz al-Din al-Qassam Brigades, died of his wounds on Saturday after Israeli jets bombed his home overnight.
Medical officials say at least 450 people have died in Gaza and 2,250 have been injured since Israel's aerial bombardment began last week.
Four Israelis have been killed in the same period by Palestinian rockets, including longer-range weapons that have hit the port of Ashdod and the desert town of Beer-sheva.
On Saturday, Israel's military said more than a dozen rockets have been fired over the border.
Palestinians also reported more Israeli air strikes across the Gaza Strip. A school was among the buildings bombed.
Israeli jets have fired more than 700 missiles into Gaza since the assault began last week.
Ayman Mohyeldin, Al Jazeera's correspondent in Gaza, said: "The Israeli military continues to pound targets everywhere in the territory. On the eighth days of attacks people here are very much terrorised by what is going on.
|Palestinian doctors attend to a wounded boy [AFP]
"The Israeli military is engaging in very aggresive psychological warfare. They have been dropping leaflets warning Palestinians that they have to flee their homes and warning that anyone who lives in area that could be a possible target that their home will be targeted as well.
"So that is causing a ripple effect of fear, but the question is where do 1.5 million Palestinians trapped in Gaza go".
Trucks carrying more than 200 tonnes of Syrian Red Crescent aid left Kura Al Assad for Gaza on Saturday as concerns for a looming humanitarian disaster grew.
Israel says that there is a humanitarian crisis in Gaza and that it has increased its shipments of goods into the territory.
Speaking to Al Jazeera, Azmi Bishara, an Israeli-Palestinian and former Knesset member, said: "Mostly, the war against such a place – slums and refugee camps - can only be a war crime.
"Whatever the military result, the political situation would be the same. What is called in American language the axis of moderation, or the moderates in the Arab world, have already had a blow, they are weaker than before.
"I think this is the only practical 'achievement' of the war that the people who are for the settlements in the region are less legitimate now and weaker than they were before the war.
Meshaal, speaking from the Syrian capital of Damascus on Friday, said Palestinians in Gaza were ready for any land offensive made by the Israelis.
"This battle was imposed on us and we are confident we will achieve victory because we have made our preparations.
"Our position is clear. We will not give in. Our resolve cannot be broken," he said.
"Our demand is also clear. The war must end, the siege lifted, and crossing points open without restriction."
|Meshaal says Hamas is prepared to handle an Israeli ground offensive [AFP]
But George Bush, the US president, in his first public comments on the hostilities, said Hamas had "instigated" Israel's war on Gaza, referring to the rocket attacks on Israel's southern towns.
"There must be monitoring mechanisms in place to help ensure that smuggling of weapons to terrorist groups in Gaza comes to an end," he said in remarks prepared for his weekly Saturday radio address.
Osama Hamdan, a senior Hamas official in Beirut, told Al Jazeera that the party to be blamed for the present situation is Israel, not Hamas.
"It's clear now that Israelis are blocking all the political solutions. The main question is supposed to be what will be the right end for this? And the clear answer is ending the occupation."
Speaking to Al Jazeera, Nir Rosen, a Beirut-based journalist, said: "There isn't very much [Hamas] can do except resist and withstand the Israeli assaults.
"These attacks are described as an Israeli retaliation which is ridiculous. Every Palestinian act of resistance is a retaliation for 60 years of occupation and dispossession.
"This use of violence is essential to Zionism, in an attempt to crush the Palestinian spirit to crush the Palestinian resolve."