The military statement said the operations destroyed "eight tunnels" and "eliminated dozens of terrorists, destroyed combat compounds and booby-trapped buildings."
The offensive in Shujaiya, which involved elite Israeli units, expanded Monday into the centre of Gaza City.
Mahmoud Bassal, a civil defence spokesman in Gaza, said there was extensive damage to "infrastructure and residential area" in Shujaiya, which had become a "ghost town".
"We are telling the world for the millionth time that the reality in the Gaza Strip is tragic and that there must be action from international and human rights institutions," he said in a statement.
Israel's army Wednesday dropped thousands of leaflets over war-torn Gaza City urging all residents to flee a heavy offensive through the main city of the besieged Palestinian territory.
The leaflets, addressed to "everyone in Gaza City", set out designated escape routes and warned that the urban area -- where UN humanitarian agency OCHA said up to 350,000 people were staying -- would "remain a dangerous combat zone".
Israeli troops launched a ground offensive at the beginning of May on Rafah, on the border with Egypt, which was then presented by Israel as the last stronghold of Hamas, but since then, clashes have increased between Israeli soldiers and Palestinian fighters in the north and centre of the Gaza Strip.
On Sunday, the war in Gaza entered its 10th month.
Hamas's October 7 attack on southern Israel that sparked the war resulted in the deaths of 1,195 people, mostly civilians, according to an AFP tally based on Israeli figures.
The militants also seized 251 hostages, 116 of whom remain in Gaza, including 42 the military says are dead.
Israel responded with a military offensive that has killed at least 38,295 people in Gaza, also mostly civilians, according to figures from the territory's health ministry.
