The battle for the Yemeni port of Aden has made it a "ghost city", the head of the ICRC in the city has told the BBC.
Robert Ghosen said medical aid was urgently needed in the city, where Shia Houthi rebels are fighting forces loyal to the government.
Aid agencies say more than 540 people have been killed in recent fighting and more than 100,000 have been displaced.
Aircraft from a Saudi-led coalition are bombing the rebels in support of the internationally recognised government.
President Abdrabbuh Mansour Hadi fled to Saudi Arabia last month as the rebels pushed south from the capital, Sanaa.
As the rebels have advanced on Aden, the port has also been shelled by Saudi forces from the sea.
Fighting escalated in the city this week, with reports of overflowing hospitals, hijacked ambulances and bodies left in the streets.
The ICRC - the International Committee of the Red Cross - says it is ready to send two aircraft to Yemen, loaded with medical supplies, but has so far been unable to do so.
On Monday, an aid flight to Yemen was held back because of logistical problems.
The World Health Organisation says more than 540 people have died in the Yemen's conflict in the last two weeks and nearly 2,000 have been injured.
The UN children's agency, Unicef, says at least 74 of the dead are children, and more than 100,000 people have been displaced.
'Nowhere to be seen'
"We are seeing a lot of people arriving dead at the hospital or dying in the hospitals," Mr Ghosen told the BBC's Today programme.
"The hospitals don't have the right supplies and the right staff," he said.
"People are nowhere to be seen, they are hiding. The economy has completely stopped," he went on, adding the streets were "littered" with rubbish and rubble from damaged buildings.
"[The city] is full of armed people from different groups fighting. This is a big city and nothing is functional," Mr Ghosen said.
Nizma Alozebi, a student from Aden, told the BBC that the violence had spread to residential areas and most shops.
"People are afraid for their belongings and their safety. It's insanity," she said.
The Houthis: Zaidi Shia-led rebels from the north, who seized control of Sanaa last year and have since been expanding their control
President Hadi: Fled to Saudi Arabia after rebel forces advanced on his stronghold in the southern city of Aden
Al-Qaeda in the Arabian Peninsula: Seen by the US as the most dangerous offshoot of al-Qaeda, AQAP opposes both the Houthis and President Hadi.
Islamic State: A Yemeni affiliate of IS has recently emerged, which seeks to eclipse AQAP
The ICRC has previously called for a 24-hour ceasefire in Aden, while Russia has also urged the UN Security Council to support a "humanitarian pause" in the air strikes.
On Tuesday, aircraft from the Saudi-led coalition bombed a military base in central Yemen, near the city of Ibb.
The raid targeted forces loyal to former President Ali Abdullah Saleh, who are fighting alongside the Houthis. The strike apparently took place near a school, and a rebel television station said three children were killed.
Meanwhile, the US says it is expediting arms deliveries to the Saudi-led coalition.
It is also increasing intelligence-sharing with the coalition to show the Houthis and their allies "that they cannot overrun Yemen by force", Deputy Secretary of State Antony Blinken said on Tuesday.
President Hadi was forced to flee Yemen two weeks ago, as the rebels advanced on Aden.
The Houthis have said their aim is to replace his government, which they accuse of being corrupt.
Saudi Arabia says the Houthis have military backing from regional rival Iran, which denies the allegation.