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At least 27 people have been killed after heavy rockets fell on residential districts of Ukraine's strategic government-held port of Mariupol in the wake of Russian-backed rebels' rejection of peace talks.

Aleksandr Zakharchenko, a rebel leader, told Donetsk city residents later on Saturday that "battle for Mariupol has begun", effectively claiming responsibility for the earlier attack, Al Jazeera's Charles Stratford reported from Donetsk.

"These attacks on Mariupol should perhaps not be too much of a surprise. The pro-Russian rebel leader Aleksandr Zakharchenko says he is not interested in any more truce talks with Ukraine," our correspondent said.

Mariupol has seen little fighting so far, but is of strategic importance. If separatists capture the city it would give them ready access to the sea.

The police chief of the war-torn region of Donetsk said on Saturday that the long-range Grad rockets hit a market in an eastern district facing roads that have come under attack from separatist militias in recent days.

 Ukraine conflict divides families

Local council of Mariupol told Al Jazeera that at least 27 people were killed and dozens more were injured in Saturday's attack.

In a statement, US Secretary of State John Kerry condemned  the "horrific assault by Russia-backed separatists".

Kerry blamed the attack on "Russia's irresponsible and dangerous decision to resupply them in recent weeks with hundreds of new pieces of advanced weaponry ... in addition to continuing operational command and control".

Mariupol lies on the Azov Sea and is the major city between mainland Russia and the Russia-annexed Crimean Peninsula.

The pro-Kiev volunteer Azov regiment based around the city said there were "many wounded" in the attack. The Mariupol administration said the rockets hit a large market in one of the city's main residential districts.

"Right now, there are problems with the cell phone network so it is impossible to call relatives who live in that part of town," Mariupol resident Eduard told the AFP news agency.

"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 attack has raised fears that Russian-backed separatist forces will try to establish a land link between Russia and Crimea.

Rebel forces have positions about 10 km from Mariupol's eastern outskirts.

A massive rebel assault on the port in August led to intense fighting that saw Kiev repel the attack at a heavy cost that soon prompted Ukrainian President Petro Poroshenko to agree to a September 5 truce.

That deal was followed by more clashes that killed at least 1,500 people and was ultimately rejected by the rebels on Friday.

The separatist leader of Donetsk vowed on Friday to escalate the nine-month campaign and seize lands in southeastern Ukraine that are currently under control of the pro-Western authorities.

Source: Al Jazeera and agencies