The UN's top humanitarian official has criticised Israel and Hezbollah for hindering access to southern Lebanon, calling the situation a "disgrace".
Agencies are looking for ways to get supplies into southern Lebanon
Jan Egeland said both sides could give aid agencies access in a "heartbeat". Hospitals in south Lebanon are also said to be low on food and fuel.
The warning came amid more violence across the Israel-Lebanon border.
Two Israeli Arabs were killed in Hezbollah rocket fire, while Israeli air strikes killed two Lebanese.
An Israeli soldier was also killed in fighting in southern Lebanon.
Israeli planes also dropped leaflets on southern Beirut, warning residents of three districts to leave immediately.
More than 1,000 Lebanese, most of them civilians, have now been killed in the hostilities, the Lebanese government has said. Some 122 Israelis, most of them soldiers, have also been killed.
Speaking at UN offices in Geneva, Switzerland, Mr Egeland said Israel and Hezbollah were preventing relief workers from saving people's lives.
"It is a disgrace really. We have not had any access for many days to the besieged population of southern Lebanon," he said.
The UN's World Food Programme (WFP) also called on both sides to allow humanitarian aid through.
"Our aid operation is like a patient starved of oxygen facing paralysis, verging on death " said Zlatan Milisic, WFP emergency co-ordinator in Lebanon.
Mr Milisic said about 100,000 people were stranded south of the Litani River.
WFP spokeswoman Christiane Berthiaume said relief supplies reached the coastal city of Sidon on Wednesday but the Israeli Defense Forces had not granted permission for a convoy to go to Nabatiyeh, north of the river.
Medical aid agency Medecins Sans Frontieres (MSF) has meanwhile warned that hospitals in south Lebanon are running out of food, fuel and medical supplies.
As the humanitarian crisis deepened, violence between Hezbollah and Israel showed no sign of easing.
Among the main developments:
- Israeli forces said they had taken control of the strategically placed town of Marjayoun - a mostly Christian town about 8km (five miles) from the border
- Hezbollah reported destroying at least 13 tanks in south Lebanon
- Israel fired about 1,000 artillery shells at the Hezbollah stronghold of Khiam, with ground battles also reported in the area
- Israeli rocketed a disused lighthouse tower carrying a television mast in west Beirut
On Wednesday the Israeli cabinet approved a plan to thrust deeper into Lebanon, towards the Litani River, up to 30km (18 miles) from the Israeli border.
Israeli officials however say the plan has been delayed.
The BBC's Christian Fraser in Beirut says it seems the timing for that push depends to a large extent on what is happening in New York, where the UN Security Council is working on a ceasefire resolution.
US ambassador John Bolton said there could be a vote on a resolution on Friday. The council's five permanent members are holding further talks to try to resolve the remaining obstacles to a final text.
The dispute is over a timetable for Israel's withdrawal from south Lebanon - France thinks Israel should pull out as Lebanese troops take over, while the US supports Israel's contention that it must stay put until a new international force can be deployed.