Fighting rages in Ukraine's east as US warns of long war

Ukraine battled Russian forces in its eastern region Tuesday while overnight missile strikes hit the southern port of Odessa, as the United States warned that Russian President Vladimir Putin is ready for a long war. 

Washington's bleak prediction came after Ukraine said its membership of the European Union was a question of "war and peace" for the whole continent as it faces up to Russia, well over two months after Moscow invaded.

Kyiv also hailed what it said was EU powerhouse Germany's change of stance on a Russian oil embargo and on supplying arms to Ukraine.

Violence raged in the south, where the missile strikes in Odessa overnight destroyed buildings, set ablaze a shopping centre and killed one person, just hours after a visit by European Council President Charles Michel.

Officials also said some 1,000 troops remain trapped in increasingly dire circumstances in the Azovstal steelworks at the devastated city of Mariupol.

Russia invaded Ukraine on February 24 -- but Ukrainian forces managed to push Moscow's forces back from Kyiv. The capital's mayor said Tuesday that two-thirds of its residents have returned.

Putin has given few hints on his plans, but US Director of National Intelligence Avril Haines said Tuesday that the Russian leader will not end the war with the Donbas campaign and is determined to build a land bridge to the Russian-controlled territory in Moldova.