Mariupol city council says more than 2,000 people have been killed since the city was besieged by Russian forces.

More than 2,000 people have died in the city of Mariupol since Russia launched its war in Ukraine, the city council has said, as the International Committee of the Red Cross (ICRC) warned that residents of the besieged port city face a “a worst-case scenario” unless the warring parties reach an agreement to ensure their immediate safety and access to humanitarian aid.

“To date, 2,187 Mariupol residents have died from attacks by Russia,” the Mariupol local council said on its official Telegram account on Sunday. Since the war in Ukraine began on February 24, it added, Russian forces have dropped about 100 bombs on the city, including 22 in the previous 24 hours.

Ukrainian authorities say the city has been subject to relentless bombardment since Russian troops surrounded it on March 2. Since then, the roughly 400,000 people who remain in Mariupol have been left with no access to water, food and medicine. Heat, phone services – and electricity in many areas – have been cut.

“The situation is catastrophic; it has been catastrophic for days,” the ICRC’s Jason Straziuso told Al Jazeera. “Even our team is collecting water from streams … but how does everyone do that … especially if you are elderly?” he asked. Straziuso said that his team members were eating one meal per day.

In a statement later on Sunday, the ICRC warned that time was “running out” for those trapped in the city.

“History will look back at what is now happening in Mariupol with horror if no agreement is reached by the sides as quickly as possible.”

ICRC president Peter Maurer called on all parties involved in the fighting to “place humanitarian imperatives first”.

The ICRC said “a concrete, precise, actionable agreement” was needed without delay so civilians wanting to leave can reach safety, and life-saving aid can reach those who stay.

Moscow has repeatedly justified its offensive in Ukraine, saying that it was conducting a “special military operation” attacking military targets. Last week though, Kyiv accused Russia of bombing a children’s hospital and a maternity ward and killing three people, while Mariupol’s local authorities on Thursday reported that city’s residential areas had been shelled “every 30 minutes”.

The capture of the port city is strategically important to Moscow as it would link Russian-backed territories in the east with Russian-annexed Crimea in the south.

Several attempts to establish evacuation corridors to allow civilians to escape the city, and to allow humanitarian aid to enter, have fallen apart as previously agreed ceasefires collapsed.

Ukrainian authorities have accused Russia of deliberately opening fire on aid convoys heading towards Mariupol. Russia has blamed Kyiv for sabotaging ceasefire agreements.

On Sunday, another attempt was under way as Ukraine’s President Volodymyr Zelenskyy said that a convoy with humanitarian aid was two hours away from Mariupol.

“We’re doing everything to counter occupiers who are even blocking Orthodox priests accompanying this aid, food, water and medicine. There are 100 tonnes of the most necessary things that Ukraine sent to its citizens,” Zelenskyy said in a video address.

The president also said that nearly 125,000 civilians from other cities have been evacuated through safe-passage corridors in one day.

Amid collapsed ceasefires and trade accusations, Mikhail Podolyak, a member of the Ukrainian negotiating team, said on Sunday that there has been some progress in the talks with his team’s Russian counterparts.

Russia is not “putting ultimatums, but carefully listens to our proposals,” he said on Twitter.