The fighting has included "unacceptable attacks on Palestinian Authority installations, institutions and personnel, and endangers civilians throughout Gaza," Mr. Ban's spokesperson said in a statement.
"Equally unacceptable is the firing by Palestinian militants of rockets into Israel, targeting and injuring civilians."
Stressing that all Palestinian factions must immediately cease all acts of violence, the statement calls on President Mahmoud Abbas, Prime Minister Ismail Haniyeh and the Palestinian Authority government to play their part to end the fighting and restore calm.
Mr. Ban "underlines the obligations on all parties involved to act in strict accordance with international human rights and humanitarian law, and to ensure that humanitarian operations can continue without impediment."
The UN Office for the Coordination of Humanitarian Affairs (OCHA) reported today that at least 37 people have been killed and 114 others injured in internal Palestinian violence since Sunday and that everyday life in Gaza City has become paralyzed as locals are now too afraid to leave their homes.
"There are no shelters for the civilian population, and most people can only seek cover inside their homes, leaving them vulnerable to stray bullets and other types of ammunition," OCHA stated in its latest update on the situation.
"Streets are barricaded and masked gunmen at dozens of impromptu checkpoints stop the few vehicles travelling on the roads for ID checks and searches," the report said, adding that access to education and health care have also been disrupted.