A Ukrainian marine commander in Mariupol has made what he described as his troops' "last address to the world" as they try to resist overwhelming Russian forces in the city.

They were outnumbered and running out of supplies, Major Serhiy Volyna said.

A Russian deadline for the surrender of Ukrainian forces has passed with no sign that the troops have complied.

The last holdouts are sheltering in the city's huge Azovstal steel plant, reportedly with 1,000 civilians.

Kyiv said there was a tentative deal to rescue some civilians from the city.

The city's mayor, Vadym Boichenko, told national TV that Ukraine had hoped to send 90 buses to evacuate about 6,000 people on Wednesday. He said around 100,000 people are trapped in Mariupol.

However, regional governor Pavlo Kyrylenko subsequently said that fewer buses than planned were able to reach trapped civilians and not many were evacuated.

"People of course gathered at the agreed meeting points, but few of them got onto the buses," he told Reuters news agency without giving specific figures.

The Azovstal Iron and Steel Works - a massive, four sq-mile (10 sq km) plant in the south-east of the city - has become the last centre of the Ukrainian resistance in Mariupol.

It is unclear how many Ukrainian troops remain in the city, but in a video message sent to the BBC, Maj Volyna, said around 500 injured troops were being cared for at the steel plant.

Maj Volyna, who leads the 36th marine battalion, said his troops were running low on supplies and that the video marked "our last address to the world. It may be our last one ever".

He said that Russian forces outnumbered his own by "dozens of times," and that while Ukrainian morale remains high, Moscow's forces "prevail in the air, in artillery, in ground troops, and in machines and tanks".

As Russian forces advanced slowly into the heart of Mariupol, the sprawling Azovstal complex became a home to thousands of Ukrainian soldiers, including fighters from the Azov battalion - a controversial national guard unit with links to the far-right.

The site is a mass of tunnels and workshops, and provides a natural advantage to defenders.

Yan Gagin, an official with the separatist Donetsk People's Republic, told Russian state news network RIA Novosti over the weekend that there is "basically another city" beneath the plant.

Russia has been bombarding the factory with artillery and air raids, and Moscow has issued two demands for the troops to surrender. An advisor to President Volodymyr Zelensky said Russia is targeting the defenders with bunker busters - colossal bombs designed to penetrate thick armour and kill targets underground.

This is the second ultimatum Ukrainian troops at the plant have faced this week. Despite this, and the vicious nature of the Russian siege, Ukraine's defence ministry said not a single soldier surrendered when a similar ultimatum lapsed on Monday.