Air raids took place in southern and south eastern areas of the Gaza Strip, as well in the northern Beit Lahia and northwestern Jabalya.
Mohyeldin said that Sunday's maneuverings have raised speculation that they are a dry run for a full attack in the coming days.
Ehud Olmert, the Israeli prime minister, said that his country was nearing its objective in the offensive but that it must fight on to achieve its goals of halting Palestinian rocket fire into Israel.
The Israeli security council is thought to be discussing whether phase three of the Gaza offensive should be implemented - a phase which will put ground troops further into the Gaza Strip.
James Bays, Al Jazeera's correspondent on the Gaza-Israel border, said: "Israel's leaders did not want to get to phase three.
"They were hoping to meet their military aims after phase one and two, achieving the mechanism they want in Gaza and stopping weapons smuggling from Egypt.
"But they feel their objectives have not been met yet. Phase three could be very dangerous for the Israeli soldiers. Hamas knows the territories very well and are preparing for the urban battle.
"Political leaders in Israel are under pressure. However, there is a strong public support for the war.
"The meeting today will look at phase three and at the end game of this operation."
The attempted advance comes after Israel dropped leaflets warning Gaza residents of a "widening offensive".
Attacks had continued during the night with Israeli tanks and infantry units moving into southwest Gaza City and exchanges of fire occurring with Palestinian fighters.
Israel claimed it shelled about 60 targets throughout the Gaza Strip overnight, hitting weapons depots, tunnels and a mosque.
At least four Palestinians were killed and dozens wounded, Palestinian medics said.
Three Palestinian rockets were fired into Israel, two hitting the southern city of Beer'sheva, without causing injuries.
About 3,700 Palestinians have 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.
Palestinian citizens have fled areas under continued Israeli shelling and regions which have received warnings of attacks.
|Three rockets were fired from the Gaza
Strip into Israel on Sunday [AFP]
Many Gazans left their homes in the Tal al-Hawa neighbourhood in southwest Gaza City shortly after dawn, witnesses said.
Fares Akram, a human rights worker in Gaza City, told Al Jazeera: "Yesterday they dropped fliers into a new area ... warning residents that the Israeli army will be escalating and intensifying its operations against what it calls terrorist elements.
"They were warning the residents to keep themselves away from any store containing weapons and away from the tunnels used to smuggle and away from the terrorist cells.
"But the residents here don't know where to go. The Gaza Strip is very small and the missiles and bombs have been landing almost everywhere. And the recent flier they try to terrify the people even more.
"The day before yesterday the tanks in northern Gaza advanced even more, forcing more people to flee their houses, including [us], because we hear so much about Israeli atrocities in the north and the south east of Gaza.
"So when we get to the new area ... fliers were dropped there ... trying to warn the people who had just evacuated their houses that the Israeli forces were continuing their campaign behind them."
Both Israel and Hamas, which rules the Gaza Strip, have ignored international calls for a cessation to fighting and Egyptian attempts to negotiate a ceasefire.
|More than 870 Palestinians and 13 Israelis have died since the offensive began [AFP]
Khaled Meshaal, Gaza's political leader in exile in Damascus, the Syrian capital, said: "The enemy has succeeded in creating a holocaust on the soil of Gaza.
"Therefore, 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.
"You have achieved nothing but killing innocent children and leaving Gaza in a sea of blood."
Meshaal also said that Hamas would not accept any truce initiative while "we are still under attack."
Talks are continuing between a delegation of Hamas leaders in Cairo with Omar Suleiman, the Egyptian intelligence chief, over a possible ceasefire agreement. Egypt is expected to call for a 48-hour truce during which negotiations can take place.
An humanitarian corridor into the Gaza Strip was opened by Israel between 0900GMT and 1200GMT, but reports of strikes in Jabalya and other areas continued during this period.
Calls have mounted for Israel to allow aid into the Gaza Strip, which has remained short of essential food and medical supplies due to a blockade of the territory by Israel for the past 18 months.
However, there remain barriers to distribution of such aid once inside the Strip, with agencies' security being poorly assured. Last week a UN employee was shot and killed by an Israeli soldier, forcing the organisation to temporarily suspend work in the region.