Israeli troops are reported to have entered the suburbs of Gaza City and are engaged in street fighting with Palestinian militants.
Witnesses said Israeli special forces had advanced several hundred metres into several neighbourhoods. Intense gunfire could be heard.
Israel says it will not call off its offensive in Gaza until the Hamas militant group stops shooting rockets into Israeli territory.
The Israeli foreign ministry told the BBC there was also no guarantee that Hamas - the group that controls Gaza - would respect any ceasefire agreement.
After talks in Egypt, a Hamas spokesman said any ceasefire deal would have to entail a halt to the Israeli attacks, a complete withdrawal of their forces and the ending of Israel's blockade of Gaza.
The Israeli military said its forces attacked more than 60 targets on Tuesday, including tunnels under the Egypt-Gaza border and rocket launching sites.
Palestinian medical officials say more than 1,000 Palestinians have been killed, around a third of them children. Israeli officials say 13 Israelis, including three civilians, have been killed.
The Al-Mizan Centre for Human Rights, a Palestinian group, says more than 90,000 Gazans have now abandoned their homes to escape the Israeli bombardment.
Meanwhile, the head of the International Committee of the Red Cross, Jakob Kellenberger, has been to the Gaza Strip to see for himself the humanitarian situation there.
Mr Kellenberger’s visit comes as the UN secretary-general, Ban Ki-moon, prepares to fly to the Middle East for talks to try to end the fighting.