As the war entered its 19th day, witnesses said the number of air strikes on Gaza City and other parts of the north was well down on the previous night, but that heavy fighting continued there.
"Tanks are shelling Palestinian fighters, who are responding with RPGs (rocket-propelled grenades). There is heavy machine-gun fire on both sides."
There were no immediate reports of casualties.
Speaking on Tuesday, Palestinian president Mahmud Abbas said Israel's offensive was "becoming more ferocious each day as the number of victims rises.
"Israel is keeping up this aggression to wipe out our people over there," he added from his base in the occupied West Bank.
Israeli special forces backed by tanks and air strikes had thrust ever deeper into Gaza's City, advancing hundreds of metres (yards) into several neighbourhoods in the south, witnesses said.
The crump of tank shells and the crackle of gunfire echoed through much of the day.
Palestinian medical sources said around 70 people were killed on Tuesday, taking the overall toll to around 975 Palestinians, with another 4,400 wounded.
Ten Israeli soldiers and three civilians have been killed in combat or by rocket attacks since December 27, when the Jewish state began its deadliest ever offensive on Gaza, ruled by the Islamist Hamas movement since mid-2007.
Israel also carried out a wave of bombing raids on the border town of Rafah, sending hundreds of people fleeing onto the streets, and those strikes continued into the night.
The military said its warplanes had attacked more than 100 targets since early on Monday morning, including 55 weapons-smuggling tunnels in southern Gaza.
Eighteen rockets and mortar rounds were fired into Israel, an army spokesman said -- barely a quarter of the number recorded at the start of the offensive. No casualties were reported.
Israel's military chief said Operation Cast Lead was making progress but warned that troops faced "complicated" conditions in Gaza City, home to more than half a million people and where Israel has little combat experience.
"We have already achieved a lot against both Hamas's infrastructure and its military wing but we still have work to be done," the chief of staff, Lieutenant General Gabi Ashkenazi, told lawmakers.
A senior official told the Ynet Internet news site that Prime Minister Ehud Olmert had "defined two objectives -- an end to Hamas fire and terror, and an end to the organisation's military build-up. As long as these objectives are not secured, we will not be under any pressure (to end the operation)."
Saying "nobody should stand there with a stop watch or try to put a gun to our head" to end the offensive, he added: "We are not seeking an exit, but rather, success. As Olmert defined it, what we need here is a strategy of success, regardless of how much time it takes."
A Hamas delegation is currently in Cairo for talks on a Western-backed proposal drawn up by President Hosni Mubarak to end the fighting.
A senior source in Cairo indicated Egypt was getting increasingly frustrated at Hamas's response so far to its initiative, saying "they need to say 'yes', now, to our plan."
A top Hamas leader, Mussa Abu Marzuk, acknowledged the movement had "substantial observations" about the initiative but said there was "still a chance" they would accept it.
Hillary Clinton, due to become US secretary of state in a week's time, said Barack Obama's administration would make "every effort" to forge peace but ruled out talks with Hamas until it recognised Israel's right to exist.
"You cannot negotiate with Hamas until it renounces violence, recognises Israel and agrees to abide by past agreements," she told a Senate confirmation hearing. "That is just for me an absolute."
British Prime Minister Gordon Brown spoke with Israeli Prime Minister Ehud Olmert and with Mubarak, pressing them "for the specific measures necessary to deliver a full and sustainable ceasefire" in line with last week's UN Security Council Resolution.
Brown's office said he was "deeply troubled" by the suffering in Gaza, urged Israel to respect its humanitarian commitments and called on Arab leaders to "say more clearly that Hamas must disarm."
Aid agencies have warned of a growing humanitarian crisis in the territory where the vast majority of the 1.5 million population depends on foreign aid and is already reeling from 18 months of punishing Israeli blockade.
"Israeli bombardment is causing extensive destruction to homes and to public infrastructure throughout the Gaza Strip and is jeopardizing water, sanitation and medical services," said a UN field report.
"As of this morning (Tuesday), 60 percent of Gazans are not receiving any power. The rest receive electricity intermittently," the Office for the Coordination of Humanitarian Affairs (OCHA) said.