Troops entering the southern Tal al-Hawa neighbourhood were met by roadside bombs, mortar and gunfire, witnesses said.
Mounting death toll
Medical sources said that 24 Palestinian fighters were killed in clashes on Sunday, taking the total number of Palestinian deaths since Israeli began its war on the territory to 885, many of them women and children.
About 4,000 Palestinians have also been wounded since the beginning of the offensive.
Thirteen Israelis have been killed during the same period, including three civilians hit by rockets fired from the Gaza Strip into Israel.
Al Jazeera's Ayman Mohyeldin, reporting from Gaza City, said that the Israeli manouevres on Sunday had raised speculation that they were planning a full attack on targets in the city in the coming days.
Israeli tanks were positioned on the edge of the city to the north and east, while a column of tanks to the south advanced only to later pull back.
The cabinet meeting was expected to include discussion of a possible "third stage" of the offensive in which the military would enter Gaza's urban areas.
However, several Israeli officials suggested that the offensive could be drawing to a close after last week's UN Security Council resolution calling for an immediate ceasefire.
"The decision of the security council doesn't give us much leeway," Matan Vilnai, the deputy defence minister, told public radio.
"Thus it would seem that we are close to ending the ground operation and ending the operation altogether."
Giroa Eiland, a former Israeli national security adviser, told Al Jazeera that there was a debate within the Israeli government and security establishment about what the goals of the operation should be at this stage.
"The main question is how to conclude and accomplish the missions," he said.
|Nearly 880 Palestinian have been killed since the Israeli offensive began 16 days ago [AFP]
"As far as I can understand one of the reasons the military option might be expended is in order to give an Israeli solution to the situation."
Amos Gilad, a senior Israeli official, was expected to travel to Cairo in the coming days to discuss a plan to end the fighting after Hamas officials met Egyptian officials on Sunday.
The Israeli military onslaught has, so far, failed to achieve the stated aim of stopping Palestinian fighters from firing rockets into southern Israel.
At least 17 rockets had been fired across the border by mid-afternoon on Sunday, but failed to cause any casualties.
Khaled Meshaal, the exiled political chief of Hamas, said Hamas would not accept any truce initiative while "we are still under attack".
"I address the Israelis and say to them; 'What have you achieved through this war you have supported? And you supported your leaders to conduct it,'" he said.
"You have achieved nothing but killing innocent children and leaving Gaza in a sea of blood."