"The shocking violence of recent days in Gaza, much of which has involved violations of international humanitarian and human rights law, has caused great alarm and sadness around the world," Mr. Ban said in a statement released by his spokesperson.
Dozens of people have been killed in recent days amid fighting between members of the Hamas and Fatah movements in Gaza, and UN officials say the clashes are worsening the already perilous living situation of many Palestinian civilians.
In his statement Mr. Ban said he was particularly concerned about the ability of the UN Relief and Works Agency for Palestine Refugees in the Near East (UNRWA), the World Food Programme (WFP) and other agencies to deliver humanitarian assistance to the majority of the estimated 1.5 million people living in Gaza.
He noted that many Palestinians remain dependent on emergency aid for their daily sustenance, and stressed that the UN remained commitment to ensuring the safety of its workers so that they can keep up their aid efforts.
"This will require the cooperation of all parties to ensure appropriate security and access conditions for the passage of humanitarian goods and personnel, both within the Gaza Strip and at key crossing points."
The UN agencies themselves have also raised the alarm, with the WFP saying it was doing the best it could under the circumstances to provide aid, and had been able to still distribute bread to hospitals. All crossing points from Gaza into Israel have been closed, and WFP estimates there are only enough food supplies in the markets to last a week.
The UN World Health Organization (WHO) reported that many of its health workers - as well as patients - have not been able to leave their homes in recent days because of the violence, while at least four hospitals have been fired upon and the emergency wards are becoming increasingly overwhelmed by the number of patients who have suffered grave injuries in the fighting this week.
Mr. Ban had a teleconference this morning with other principals of the Quartet, the diplomatic grouping that comprises the UN, the European Union, Russia and the United States. The Secretary-General's spokesperson Marie Okabe told reporters that he would remain in close contact with the other Quartet members in the days ahead.
In the statement Mr. Ban expressed deep disappointment at the failure of the Palestinian National Unity Government, "and the violence, destruction and fragmentation that has brought about its demise."
He added that he renewed his support to Palestinian President Mahmoud Abbas "as he moves to discharge his responsibilities under the Palestinian Basic Law."