"Most of our partners have stopped giving services in the last 24 hours because of the deteriorating security situation," Alberto Oggero from the European Commission Directorate for Humanitarian Aid told IRIN.
Another EC official said the body had advised partners to be exceedingly careful, and reduce activities to an absolute minimum to ensure the safety of their staff.
Since 11 June, two UN employees, Hassan Ahmad El Leham and Abdul Fateh Hussein Abu Ghali, have been killed in the crossfire, and two others seriously wounded.
The situation has also led to the effective closure of the Rafah crossing, on the Egyptian border, and the Erez crossing into Israel. In addition, Karni crossing, used to transport goods, including fuel and humanitarian aid, is also not operating.
"A prolonged closure will lead to shortages of basic supplies in Gaza," said David Shearer, head of the UN's Office for the Coordination of Humanitarian Affairs (UN OCHA) for the occupied Palestinian territories in Jerusalem.
"We tried to convince the NGOs to stock up their warehouses in Gaza, in case a day like today came," said Shlomo Dror, from the Israeli Ministry of Defense's humanitarian coordination section. "In the current situation, there is literally no one to coordinate with on the Palestinian side," he added.
Liz Sime, from CARE International, said her organisation has put operations on hold. "As soon as it is safe, we will move medical supplies from our Gaza warehouse to hospitals," she says.
The current situation is affecting more than one million Palestinians who receive aid from different organisations and agencies.
More than 90 people have been killed, and over 400 wounded in the recent fighting.
Hamas TV showed its militants arresting members of various Palestinian Authority security organs loyal to President Mahmoud Abbas of Fatah. In some cases, the prisoners were executed in the streets.
The fighting has caused the evacuation of the Al Quds hospital in Gaza City, associated with the Palestine Red Crescent Society (PRCS). "We evacuated patients from the PRCS to other hospitals. The hospital is not functioning, as all networks, including power and water, were damaged," said Iyad Nasr from the International Committee of the Red Cross (ICRC), one of the few humanitarian organisations still active in Gaza.
Shifa Hospital, the main medical centre in the Gaza Strip, is in dire need of blood supplies, say medical officials.
The fighting has also made it difficult for ambulances to transport the injured. According to UN OCHA, at least six Ministry of Health ambulances were hit during the clashes while on duty. The ICRC, which coordinates ambulance movement, said it had encountered long delays while trying to secure security guarantees for medical staff.
Certain areas of Gaza were without water supply on Thursday afternoon, although in other areas, where Hamas had managed to gain full control, some shops were reopening and people were venturing out into the streets again.
"The situation is very tense and difficult. We will have to wait and see. Right now it is moment by moment," said one aid worker involved in coordination efforts.
Observers are concerned that the intense fighting may soon spread into the West Bank, where there are signs of unrest.