Israel’s Defence Minister Yoav Gallant says their troops are “in the heart of Gaza City.”
Gallant says the Israel Defense Forces “stormed” the city from the north and south in coordination with land, air and sea troops.
Earlier, the World Health Organization said the level of death and suffering in the war between Israel and Hamas is hard to fathom.
A spokesman for the UN agency pointed to the death tolls on both sides, and said an average of 160 children are now being killed each day in Gaza.
Earlier, dozens were reported killed by Israeli air strikes in the southern Gazan cities of Khan Younis, Rafah and Deir al-Balah.
The Israel Defense Forces have not commented on the strikes – but said they took control of a Hamas stronghold in northern Gaza in recent fighting.
In Israel, people across the country have been marking one month since the Hamas attacks on 7 October, which saw 1,400 people, mostly civilians, killed, and more than 200 people taken hostage.
More than 10,300 people have been killed in Gaza according to the Hamas-run health ministry, including more than 4,100 childre