The 'Mariupol' garrison has fulfilled its combat mission," the general staff of Ukraine's armed forces said in a statement.
"The supreme military command ordered the commanders of the units stationed at Azovstal to save the lives of the personnel... Defenders of Mariupol are the heroes of our time," it added.
Some 600 troops are thought to have been inside the steel plant.
"We hope that we will be able to save the lives of our guys," Ukrainian President Volodymyr Zelensky said in an early morning address.
"There are severely wounded ones among them. They're receiving care. Ukraine needs Ukrainian heroes alive.
It's not over in Mariupol yet - Ukrainian officer
Oleksandr Danylyuk, a former Ukrainian national security chief and finance minister, currently serving as an officer in the Ukrainian army, has been talking to BBC Radio 4's Today programme about the situation at the steelworks.
He won’t say exactly how many remain at the plant, but says there are many more left there, some of them wounded.
"It's a relief, but it's not the end."
Their main mission is completed and their lives need to be saved, he says.
Russia controls Mariupol but they don't control the steel plant, though the strategic importance of the plant is minimal at this stage, he adds, so it's rather symbolic for Russia to take full control of the city.
"But that symbolic action will cost them a lot of lives."
Ukraine military lauds Mariupol defenders as 'heroes of our time'
The Ukrainian military has lauded the Ukrainian fighters who defended the Azovstal steel plant in the besieged southern city of Mariupol, calling them "heroes of our time" and that they would be remembered "forever in history".
Hundreds of fighters had been holed up in the tunnels beneath the massive industrial plant, defending the last Ukrainian stronghold in the city.
The strategically located port city had come under massive bombardment from Russian forces early in the invasion.
Taking the city would have allowed Russia to bridge the Crimean region, which had been annexed by Russia, and the Donbas region, which is led by pro-Russian separatists.
The last stand at Azovstal in Mariupol gave Ukraine "the opportunity to prepare and create the defensive frontiers on which our troops are still present today and give a decent counterpoint to the aggressor", said Ukraine's general staff of the armed forces in a Facebook update.
"We got the critically needed time to build reserves, regroup forces, and get help from partners."
