The four gathered in Berlin for evening talks to assess progress in the truce deal agreed in February between the Ukraine government and pro-Russian rebels to end a conflict that has killed more than 6,000 people over the past year.
At stake for Moscow is the easing of punishing Western sanctions introduced as separatist insurgents, allegedly operating with Russian military assistance, seized control of a swathe of territory in the east.
He said the Berlin talks were aimed at shoring up "a certain calming of eastern Ukraine" in the last two months while moving forward with a political process laid out in the agreement reached in the Belarussian capital Minsk.
Steinmeier said the group aimed in particular to make progress "on how humanitarian aid in eastern Ukraine can finally be delivered" to the long-suffering population there, and a path toward new elections.
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After weeks in which the ceasefire agreed in the Belarussian capital Minsk appeared to be largely holding despite isolated skirmishes, clashes seemed to be mounting in flashpoint areas.
European OSCE monitors reported "renewed intensive fighting" yesterday around the rebel stronghold of Donetsk, with more than 1,166 explosions in under six hours, mainly from artillery and mortar fire.
In accordance with the Minsk deal, the two sides claim to have withdrawn heavy arms from the frontline but the OSCE said "weapons with a calibre larger than 100mm were used by both sides during the fighting".
NATO believes Russia has supplied more troops and weapons to the rebels, an unnamed alliance official was quoted as saying at the weekend by German daily Frankfurter Allgemeine Zeitung.