UN Secretary-General Ban Ki-moon has condemned a deadly rocket attack in Ukraine's government-held port of Mariupol and denounced "provocative statements" made by pro-Russian separatist fighters.

Ban's remarks came on Saturday after pro-Kremlin rebels announced a major new offensive and heavy rocket fire killed at least 30 people and wounded around 100 in Mariupol, a strategic port linking separatist territory with Russian-occupied Crimea.

Ban "strongly condemns today's rocket attack on the city of Mariupol," a statement from his spokesman read.

"He notes that rockets appear to have been launched indiscriminately into civilian areas, which would constitute a violation of international humanitarian law."

The United Nations chief also condemned Friday's "unilateral withdrawal from the ceasefire by rebel leadership, and particularly their provocative statements about claiming further territory".

He said the withdrawal constituted a violation of commitments under September's Minsk accords, which ordered the removal of heavy weapons and a truce in a bid to end the nine-month conflict that has cost more than 5,000 lives.

"Ukraine's peace, territorial integrity and stability, intrinsically linked to that of the broader region, must be urgently restored," the statement added.

Alexandre Zakharchenko, leader of the self-declared Donetsk People's Republic, earlier announced that the rebels were launching an offensive on Kiev-controlled Mariupol.

The Ban statement did not say who was responsible for the rocket fire.

Meanwhile, the UN's Security Council (UNSC) tried to put together a statement on Mariupol, at Britain's urging. But Russia, which is accused by the West of aiding separatists, blocked the effort, according to Western diplomats.

Ban "issues a strong statement on Mariupol attack but Russia blocks similar statement by the UN Security Council," British Ambassador Mark Lyall Grant tweeted.

Lithuanian Ambassador Raimonda Murmokaite also took to Twitter to criticise Russia, saying: "'DPR' chief Zakharchenko admits onslaught on Mariupol but Russia continues to shield its proxy, so no Security Council statement."

A Western diplomat privately described the failure to agree a text as "disappointing," saying the effort had been blocked "as the Russian federation were against including a reference to a public statement on an offensive on Mariupol, which had been made by a separatist leader".

Russia denied the charges, and blamed Britain for blocking the statement.

"The consensus has not been reached... because the delegation of the UK insisted on condemnation of some of the self defense forces' statements," a spokesperson for Moscow's mission to the United Nations said in a statement.

"The UNSC Western members throughout the entire conflict have been refusing to condemn any statements and actions -- often very aggressive -- made by the Kiev authorities."