Photos of the destruction in Mariupol were shared on social media.Twitter/MFA Ukraine

Ten people, including children, are feared to have been killed after pro-Russian rebels fired heavy Grad rockets into a residential area in the Ukraine government-held port city of Mariupol, on Saturday.

The long-range rockets hit a market area in the city and left "many wounded", and the Ministry of Foreign Affairs of Ukraine posted pictures of destruction on Twitter, also claiming that children were among the dead. 

"As a result of shelling by rebels of a residential sector of Mariupol ... ten people have been killed," police chief Vyacheslav Abroskin said through his social media account.

Several buildings have been destroyed in the rocket firing, some reports suggest. While Kieve has put the blame on the pro-Russian militia, the rebel leaders have dismissed the allegation.

"Our militias have no weapon systems near Mariupol that would be able to shell that region. Our positions are simply too far away," a spokesman of the militia headquarters in Donetsk said, according to

However, rebel forces are said to have positions just 10 kilometers (six miles) from Mariupol's eastern outskirts, according to The Associated Press.

The attack comes days after rebel shelling at a bus stop in Donetsk left 13 dead and several injured.

Separatists have vowed to step up their offensive against Kiev, with the main pro-Russian rebel leader in eastern Ukraine announcing that they will not undertake ceasefire talks.