A major offensive in eastern Ukraine by rebels allegedly backed by Russia has marked a dangerous new stage in the nine-month conflict and dashed hopes for a truce, pressuring Western nations to act.

A deadly rocket attack on the port city of Mariupol on Saturday highlighted a week-long rebel advance that has seen the separatists take the long-disputed Donetsk airport and pledge to conquer more territory.

U.S. President Barack Obama vowed on Sunday to ramp up pressure on Russia after rocket attacks blamed on Kremlin-backed Ukrainian rebels killed 30 and injured 95 more.

Saturday's surprise assault on the strategic eastern Ukrainian port of Mariupol threatened to open a new front linking separatist territory near the Russian border with the Black Sea peninsula of Crimea that Moscow annexed in March.

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

Ban's remarks came 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.

U.S. Secretary of State John Kerry on Saturday called on Russia to "immediately" stop backing Ukrainian separatists after at least 30 people were killed in the strategic port of Mariupol in a major escalation of the fighting in eastern Ukraine.

"We call on Russia to end its support for separatists immediately, close the international border with Ukraine, and withdraw all weapons, fighters and financial backing," Kerry said during a visit to Zurich.

The European Union is considering an emergency meeting to discuss the Russia-Ukraine conflict after rocket attacks killed at least 30 people in Ukraine's strategic Maruipol port on Saturday. 

Latvia, which holds the EU's six-month rotating presidency until July, called for an emergency meeting of the EU foreign affairs council next week.

Pro-Kremlin rebels announced a major new offensive on Saturday after heavy rocket fire killed at least 30 people in a strategic government-held Ukrainian port linking separatist territory with Russian-occupied Crimea.

The local mayor's office said 97 people were also wounded in the city of Mariupol by dozens of long-distance rockets that smashed into a packed residential district early in the morning and then again shortly after noon.

The European Union called Friday on Moscow to "assume its responsibility" in ending the separatist war in Ukraine.

"Time is running out in eastern Ukraine where the escalation of fighting has caused far too many civilian as well as military casualties," EU foreign policy chief Federica Mogherini said in a statement.

Russian President Vladimir Putin on Friday accused the Ukraine government of ordering a major new offensive against pro-Russian rebels in the separatist east that has claimed dozens of lives in the past few days.

"Kiev authorities have given an official order to begin large-scale combat operations" along almost the entire frontline with pro-Russian separatists, Putin said in a meeting with his security council.

Pro-Russian rebels on Friday vowed to conquer more territory in eastern Ukraine and ruled out peace talks after Kiev retreated from a long-disputed airport, casting aside Europe's latest push for a truce.

The defiant comments from Donetsk separatist leader Alexander Zakharchenko came as Ukraine renewed allegations of Russian army units fighting with rebels across the frontline dividing the war-torn country's industrial east.

Pro-Russian rebels cemented their hold Friday on a long-disputed airport ceded by Ukrainian troops during an upsurge in clashes that killed nearly 50 people and punctured Europe's latest push for peace in the nine-month war.

The deadliest day of fighting since the signing of an increasingly irrelevant September truce also saw Moscow and Kiev on Thursday trade bitter blame for a trolleybus shelling in the rebel stronghold of Donetsk that killed 13 mostly elderly passengers.