Ukrainian president Volodymyr Zelensky said the country's army was not ready to try to break through the siege of the port city by force. But he told an evening news conference that Kyiv had every right to do so.
The attack on Mariupol has raged for weeks as Russia seeks to capture a city seen as vital to its attempts to link the eastern Donbas region with Crimea, the Black Sea peninsula Moscow seized in 2014. It has been the biggest battle of the conflict so far.
Moscow-backed separatists have held territory in the Donbas region for years.
In the Black Sea port city of Odesa, at least eight people were killed, Zelensky said. Two missiles struck a military facility and two residential buildings and two more were destroyed on Saturday, the Ukrainian armed forces said.
The death toll could not be independently verified. The last big strike on or near Odesa was in early April.
"The only aim of Russian missile strikes on Odesa is terror," Ukrainian Foreign Minister Dmytro Kuleba wrote on Twitter. Russia has denied targeting civilians in its "special military operation" that began on 24 February.
The Russian defence ministry said it used high-precision missiles on Saturday to destroy a logistics terminal in Odesa where a large number of weapons supplied by the United States and European nations were being stored.
It also said Russian forces had killed up to 200 Ukrainian troops and destroyed more than 30 vehicles on Saturday.
Russian General Rustam Minnekayev on Friday said Moscow wanted control of the whole of southern Ukraine, comments Ukraine said indicated Russia had wider goals than its declared aim of demilitarising and "denazifying" the country.
Kyiv and the West have called the invasion an unjustified war of aggression.
Russian forces have besieged and bombarded Mariupol since the early days of the war, leaving in ruins a city usually home to more than 400,000 people. A new attempt to evacuate civilians failed on Saturday, an aide to Mariupol's mayor said.
Russia's defence ministry on Friday said Mariupol's last fighters had been "securely blockaded" at the steel plant. On Thursday, president Vladimir Putin had declared the city "liberated", declaring that troops would not storm Azovstal.
Oleksiy Arestovych, a political adviser to Zelensky, said Ukrainian troops in the steel complex were holding out and attempting counterattacks. More than 1000 civilians are also in the plant, according to Ukrainian authorities.