At least 20 people were killed by shelling in the east Ukrainian port city of Mariupol on Saturday, regional police said, as a rebel leader said separatists were launching an offensive on the city, the news agency RIA reported.
The separatists have rejected more peace talks and fighting has surged to its most intense in months. The United Nations said on Friday that 262 had been killed in the previous nine days.
"Today an offensive was launched on Mariupol. This will be the best possible monument to all our dead," RIA quoted rebel leader Alexander Zakharchenko as saying at a memorial ceremony in the rebel-held city of Donetsk.
He said separatists plan to encircle Debaltseve, a town north-east of Donetsk, in the next few days, the Russian news agency Interfax reported him as saying at the same event.
Mariupol city council and regional police said rebels fired rockets from long-range GRAD missile systems killing at least 20 and injuring 83. Interfax earlier said rebels had denied the attack.
Government-controlled Mariupol, on the Sea of Azov, lies on a coastal route from the Russian border to Crimea, which was annexed by Russia from Ukraine last March.
Prime Minister Arseny Yatseniuk condemned the incident as a deliberate attack on peaceful citizens by the rebels, but said the real threat lay beyond separatist territories.
"The world needs to stop the Russian aggressor threatening Ukraine, Europe and global security .. The problem is in the hero-town of Moscow - Kremlin, Vladimir Putin," he said at a meeting of security and defense chiefs.
Despite international calls for a ceasefire, Zakharchenko vowed on Friday that his forces would push on with a new offensive, as the UN said the conflict, which began in east Ukraine more than nine months ago, was now in its "most deadly period" since a peace deal was agreed last September.
At the defense meeting in Kiev, Ukrainian Defence Minister Stepan Poltorak said in the past 24 hours there had been a serious escalation in fighting at frontlines across the conflict zone.
"Starting from Luhansk region and ending in Mariupol, everywhere illegal armed groups together with Russian units are going on the offensive," he said.
In Mariupol, the attack started in the early morning, 76-year-old pensioner Leonid Vasilenko, who lives in the eastern suburbs of Mariupol, said by telephone.
"The walls were shaking, the window frames were shaking, paint started to crumble off the house. I hid in the basement. What else can you do? I took the dog and the cat. In the basement you could hear the earth tremble," he said.
The regional police said 20 people had been killed, while city authorities reported a further 83 were injured.
President Petro Poroshenko said last week Russia had 9,000 troops inside Ukraine and called on Moscow to withdraw them, blaming it for an armed aggression. Moscow denies sending forces and weapons to east Ukraine, despite what the West says is irrefutable proof.
On Friday Russian President Vladimir Putin blamed "criminal orders" by Ukrainian leaders on Friday for the surge in the conflict, which has killed over 5,000 people.