Witnesses and Palestinian security officials said the troops entered the city via the Shejaya neighbourhood.
The Israeli forces took two routes, from the Karni and Nahal Oz truck depots between Israel and the Gaza Strip.
'Halt deadly assault'
Earlier, Palestinian president Mahmud Abbas called on the international community to halt the deadly assault in Gaza after seven Palestinians were killed as Israel pressed on with its bloody offensive in Gaza and Hamas confirmed a captured soldier was alive.
Israel waged fresh air and ground attacks on northern Gaza, one day after reoccupying land in the deadliest 24 hours in the territories for four years with 30 Palestinians and one Israeli soldier killed since Thursday.
Mr Abbas urged the world to stop Israel's "inhumane aggression" to give mediators a chance to free a soldier, whose capture ignited the escalation 12 days ago.
Capping a day of attacks, Israeli forces killed a Palestinian in the northern Gaza town of Beit Lahiya when an Israeli helicopter gunship fired two missiles on a house, local medical and security sources said.
Six other Palestinians were killed by Israeli forces exchanges of fire, air strikes and tank fire, while an 11-year-old boy also died of wounds sustained in an Israeli shooting a day earlier near Beit Hanun in northern Gaza.
In the occupied West Bank, another Palestinian militant was shot dead in clashes with Israeli forces in Nablus.
Soldier still alive
Hamas warned that the assault was complicating the case of a captive Israeli soldier, Gilad Shalit, who it said was being well treated.
The movement, whose armed wing claimed joint responsibility for the June 25 attack when Shalit was snatched, said the "soldier Gilad is being well treated, in a humane manner in keeping with the values of our religion".
Israel however flatly ruled out any negotiations with the Islamists.
"I have just spoken to Prime Minister Ehud Olmert and our position remains unchanged: we refuse to negotiate with Hamas and (Palestinian) prisoners will not be released," Interior Minister Roni Bar-On said.
Israel's chief of staff Dan Halutz warned that militants had and would "pay a heavy price" if they continue their attacks, maintaining that "40 terrorists" had been killed in the offensive.
In the biggest escalation of the crisis since the soldier was abducted, Israel sent troops deep into the northern Gaza Strip on Thursday, effectively creating a buffer zone in a territory from which it withdrew last September.
Israel has vowed to use everything in its power to increase the pressure on the embattled Hamas-led government to free the 19-year-old corporal and to stop rocket attacks.
Mr Abbas said, however, that continued Israeli aggression was hindering Palestinian efforts together with "Arab parties, particularly Egypt" to return the soldier to his family.
"They still believe an agreement is possible," he said, calling on militants to stop firing rockets at Israel in a bid to ease the crisis.
Seventeen rockets have been fired since the latest offensive began.
Stop disproportionate force: Annan
UN chief Kofi Annan has called for an immediate stop to what he called Israel's "disproportionate use of force" in Gaza but also pressed for the release of an Israeli soldier snatched by Palestinian militants.
"I call again for an immediate halt to the disproportionate use of force by Israel, which has already killed and wounded many civilians, for the release of Israeli army corporal Gilad Shalit and for the cessation of rocket fire into Israel," he said in a statement.
"These measures are an absolute prerequisite for defusing the tensions which are escalating every day," said the UN chief.
Mr Annan also appealed to the 15-member Security Council to take "a clear position" on the situation.
The council has been debating a draft resolution demanding an immediate withdrawal of Israeli forces from Gaza and the release of detained Palestinian officials.
The United States, Israel's closest ally, described the text as "unbalanced".