At least 20 people have been killed and dozens injured in rocket attacks by pro-Russian rebels in eastern Ukraine's government-held port of Mariupol, police there say.
Grad rockets hit a market in a residential eastern area, the police chief said.
The main eastern Ukraine rebel leader said an offensive against Mariupol had begun, RIA news agency reported.
Since April, more than 5,000 people have died in fighting in the east.
The rebels have seized a large swathe of the Donetsk and Luhansk regions. More than a million people have been displaced.
The rebel leader, Alexander Zakharchenko, said on Friday that he did not want truce talks with the government.
A ceasefire agreed in Minsk in September but never fully took hold. Many hoped that the lower level of hostilities it introduced would last, but the BBC's David Stern says that the fighting is beginning to approach what was seen last summer.
Mariupol has a population of 500,000 and is in a highly strategic position, sitting between rebel-held eastern areas and Crimea, which was annexed by Russia last March. The city saw heavy fighting in August.
Our correspondent says that if the hostilities move to Mariupol it will signal a major escalation in the fighting.
Unverified video footage on Saturday indicated that a number cars, houses and apartment buildings had been struck and were in flames.
Our correspondent says the attack appeared to come from a multiple-rocket launcher, which fires a large number of missiles over a spread-out area.
Interfax news agency quoted the defence ministry of the rebel Donetsk People's Republic as denying involvement.
"This is blatant misinformation and a lie. Rebel forces did not open any fire in the direction of Mariupol, especially not on residential areas," it was quoted as saying.
One resident told Agence France-Presse by telephone: "Obviously, everyone in the city is very scared. The rebels have already seized the airport. And now they are starting to destroy Mariupol itself."
The US ambassador to Ukraine, Geoffrey Pyatt, tweeted: "Today's indiscriminate shelling of Mariupol part of an apparently Russian-backed general offensive in complete violation of Minsk agreements."
On Friday, rebel military spokesman Eduard Basurin said 24 rebel troops had been killed and 30 wounded in recent fighting. He called it "the heaviest losses in our ranks" in a 24-hour period.
In another development, the rebel mayor of Pervomaysk, west of Luhansk, has been killed, reports say.
The body of Yevhen Ischchenko was found in a car. Three other men were apparently killed along with him. The local rebel leadership blamed Ukrainian agents, but other sources said it was the result of infighting.
Ukraine, Russia, France and Germany have all issued calls for an end to the fighting.
Ukraine and its Western allies say Russian regular troops are fighting alongside the separatists, using Russian heavy artillery and tanks. Moscow insists that only Russian "volunteers" have joined the rebels.
Ukraine: the human cost
- Some 5.2 million people live in conflict-affected areas and 1.4 million are considered "highly vulnerable and in need of assistance"
- More than a million people have fled their homes with 633,523 living as displaced persons within Ukraine and 593,622 living outside Ukraine, mostly in Russia
- More than 5,000 people have been killed in the fighting and more than 10,300 injured
Source: UN report of 9 January for refugee figures; news reports for casualty estimates
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