Russian President Vladimir Putin has publicly shown his support for Kiev's peace plan, calling on both sides in eastern Ukraine to cease fighting and negotiate a compromise.

Putin said on Sunday that such a compromise should guarantee the rights of the Russian-speaking residents of eastern Ukraine, who should feel they were "an integral part" of their own country.

In a statement earlier in the day, Putin told his German and French counterparts that he supported Ukrainian President Petro Poroshenko's peace plan which began last Friday, adding that it should be backed up with a de-facto ceasefire agreement.

"After the Russian government too referred to the cease-fire in positive terms, the interlocutors emphasised the need for all sides to abide by it now and for a political dialogue to be put in motion," German Chancellor Angela Merkel's office said.

Putin's public comments, which followed ceremonies commemorating the Nazi invasion of the Soviet Union on June 22, 1941, were more specific.

In Kiev, Poroshenko called for peace, but urged his compatriots to stand strong and united.

Continued fighting

However, fighting has continued through the weekend with clashes between Ukrainian troops and armed separatists.

Putin said in a statement that artillery was used in overnight fighting in the east, urging Kiev to cease fighting and begin dialogue with the rebels. 

The Associated Press news agency reported on Sunday that Ukrainian nationalists clashed with police officers outside a Russian Orthodox church in the capital city of Kiev. 

"Unfortunately, what we are seeing ... tells us that the fighting is ongoing and last night we saw some active use of artillery from the Ukrainian side," he said.

"We need to ensure that all fighting is stopped," he said, reiterating his support for Poroshenko's ceasefire and peace plan.

The fighting in Ukraine's Russian-speaking east erupted in April after street protests in the capital Kiev toppled the Moscow-backed leader Viktor Yanukovich.

Russia subsequently annexed Ukraine's Crimean peninsula and the West has accused Russia of supporting the separatists.