More than 400 Palestinians have been killed in clashes mainly between militias affiliated to the Hamas and Fatah political parties in the past 14 months.
Inter-Palestinian violence, some of it clan-related rather than political, is accounting for at least as many Palestinian deaths as Israeli military action, the UN reported this year.
In the first three months of this year, 119 Palestinians were killed by other Palestinians compared to 34 fatalities caused by Israel, the UN's Office for the Coordination of Humanitarian Affairs (OCHA) reported this month.
Nine more Palestinians have been killed since Sunday and more wounded in exchanges of gunfire across Gaza City and the northern Gaza Strip as cracks appeared in the Palestinian Unity Government, in place since late February.
Interior Minister Hani Qawasmi resigned on Monday saying that he had not been given adequate authority to maintain security. Palestinian Prime Minister Ismail Haniya has now taken personal control of security in Gaza.
While the rival Palestinian factions agreed another truce on Monday night to end two days of fighting, according to government spokesman Ghazi Hamad, past agreements have not held and sporadic gunfights have occurred since.
The International Committee of the Red Cross (ICRC) said it would continue its activities in the Gaza Strip in the event of renewed fighting - and added that it would be closely monitoring the ability of emergency medical staff to get to wounded Palestinians and the security situation at Gaza hospitals.
"Ambulances must be allowed to get to the wounded and in previous clashes they have been held up at informal checkpoints. We have met with the different groups to try to make sure it does not happen again," said ICRC spokesman Bernard Burrett, speaking to IRIN from Jerusalem.
On Sunday, the various armed militias had again set up checkpoints at strategic junctions in Gaza City, with masked gunmen checking cars.
Gaza's hospitals have also been the scene of clashes in the past - and Burrett said this was also an area of concern.
"We do not accept that weapons are carried inside hospitals. Maybe they can set up some kind of perimeter security - but there can be no fighting inside the hospitals," he said.
He added that the ICRC was well stocked with medical supplies and had distributed 'war wounded' kits containing advanced equipment and drugs specifically to deal with gunshot and explosion injuries.
"We have sufficient medical supplies inside the Gaza Strip and we could reinforce them if we needed to. We are coordinating closely with the Palestinian Ministry of Health and can move supplies between Ramallah in the West Bank and the Gaza Strip if we need to," Burrett said.
UN under fire
Meanwhile, UN agencies have added sheet metal to reinforce the outer gates to their three compounds inside Gaza City after gunmen first attempted to shoot John Ging, the head of the UN Relief and Works Agency (UNRWA) in March and this month opened fire at an UNRWA sports event for children in the southern town of Rafah, killing one and injuring eight, including two children.
UNRWA now has a maximum of 10 international staff in the Gaza Strip at any one time - but Stuart Shepherd, OCHA's humanitarian affairs officer, said OCHA would continue with its programme of assistance.
UNRWA was set up to provide essential services such as food, health, education and waste disposal for Palestinian refugees. The majority of Gaza's 1.3million population are registered refugees.
"Agencies are still fulfilling their mandate using local partner organisations and Palestinian members of staff. So pulling out all international staff would have a more symbolic than practical effect," said Shepherd.
"But the threat of kidnapping is real and part of our daily lives in Gaza."
The strip's woeful economic situation was contributing to a breakdown of social structure and law and order and fuelling a growing sense of hopelessness among Gaza residents, Shepherd said.
The Palestinian Authority (PA) is under an international economic embargo until it recognises Israel and renounces violence.
"There's a complete despair. Poverty is at 80 per cent, unemployment at 40 per cent, exports are not at their full potential and the boycott is holding," he said.
"In this situation, people have fallen back on their family and tribal loyalties."