Residents feared the barrages presaged an Israeli ground operation in the south of the Palestinian territory that would pen them into a shrinking area and possibly try to push them across into Egypt.
The Gaza health ministry said at least 193 Palestinians had been killed and 650 wounded since the truce ended on Friday morning - adding to the more than 15,000 Palestinian dead since the start of the war.
Speaking in Dubai, Harris said Israel had a right to defend itself but international and humanitarian law must be respected and "too many innocent Palestinians have been killed".
"Frankly, the scale of civilian suffering, and the images and videos coming from Gaza, are devastating," Harris told reporters.
She also sketched out a US vision for post-conflict Gaza, saying the international community must support recovery and Palestinian security forces must be strengthened.
Israel will seek a "security envelope" to prevent Hamas from being on its border, an official says. (EPA PHOTO)
"We want to see a unified Gaza and West Bank under the Palestinian Authority, and Palestinian voices and aspirations must be at the centre of this work," she said, adding that Hamas must no longer run Gaza.
The Palestinian Authority governs parts of the occupied West Bank.
Hamas seized control of the Gaza Strip in 2007 from Palestinian President Mahmoud Abbas' mainstream Fatah party and has ruled the enclave ever since.
Israel has vowed to wipe out Hamas once and for all, saying the Islamist group is bent on its destruction.
Mark Regev, a senior adviser to Israeli Prime Minister Benjamin Netanyahu, said Israel did not want to see Gaza's civilians caught in the crossfire.
"Israel is targeting Hamas, a brutal terrorist organisation that has committed the most horrific violence against innocent civilians. Israel is making a maximum effort to safeguard Gaza's civilians," Regev said.
He said that when the war was over, Israel would seek a "security envelope" with special zones and arrangements to prevent Hamas from being positioned on its border.
Throughout Saturday morning, a steady stream of wounded people were carried into the Nasser Hospital in Khan Younis, some receiving treatment on the floor.
The head of the International Committee of the Red Cross said the renewed fighting was intense.
"It's a new layer of destruction coming on top of massive, unparalleled destruction," Robert Mardini told Reuters in Dubai.
With conditions inside Gaza reaching "breaking point," in Mardini's words, the first aid trucks since the end of the truce entered from Egypt through the Rafah crossing on Saturday, Egyptian security and Red Crescent sources said.
A senior official said Israel would facilitate the provision of humanitarian aid to Gaza's civilians.
The warring sides blamed each other for the collapse of the seven-day truce, during which Hamas had released hostages in exchange for Palestinian prisoners held in Israeli jails.
Israel said it had recalled a team from Qatar, host of indirect negotiations with Hamas, accusing the Palestinian faction of reneging on a deal to free all the women and children it was holding.
French President Francois Macron meanwhile said he was heading to Qatar to work on a new truce.
Israeli air strikes have hit several locations in the southern part of the Gaza Strip. (EPA PHOTO)
The deputy head of Hamas, however, said no prisoners would be exchanged with Israel unless there is a ceasefire and all Palestinian detainees in Israel are released.
Saleh Al-Arouri told al-Jazeera TV that Israeli hostages held by Hamas are soldiers and civilian men who previously served in the army.
The conflict broke out on October 7 when Hamas militants crossed into southern Israel and killed 1200 people, mostly civilians.
More than 200 hostages were taken back into Gaza.
Israel responded with a bombing campaign and a ground offensive in the north, destroying swathes of Gaza.
The southern part of Gaza including Khan Younis and Rafah was being pounded on Saturday.
Residents said houses had been hit and three mosques destroyed in Khan Younis.
Displaced Gazans have been sheltering in Khan Younis and Rafah because of fighting in the north but residents said they feared Israeli troops were preparing to move south.
