The bloc has so far ordered visa bans and asset freezes for officials but refrained from imposing broader economic sanctions on Russia.
Ahead of the EU foreign ministers meeting in Luxembourg on June 23, British Foreign Secretary William Hague said the EU will be able to agree further measures at a summit of EU leaders on June 27, if necessary.
He said Moscow must be in "no doubt" it faces further sanctions.
Swedish Foreign Minister Carl Bildt accused Russia of "conducting a propaganda war with full speed," adding that Moscow must face further sanctions unless it changes course.
Meanwhile, the European Council said it has finalized technical preparations ahead of the signature of an Association Agreement with Kyiv in Brussels on June 27.
WATCH: Police violently broke up a demonstration of Maidan supporters in the eastern city of Kharkiv on June 22. Members of the Hryfon special police unit attacked Ukrainian activists who attempted to prevent a pro-Russian rally in the city center.
In Ukraine, the governor of the eastern Kharkiv region, Ihor Baluta, has called on residents to respect the peace plan put forth by President Petro Poroshenko.
Baluta on June 23 urged his people to avoid conflicts after pro-Ukrainian and pro-separatist activists clashed in the city of Kharkiv on June 22.
Russian Foreign Minister Sergei Lavrov and his German counterpart, Frank-Walter Steinmeier, discussed the situation by telephone in Ukraine late June 22.
The Russian Foreign Ministry on June 23 released a statement saying the two had agreed "a stable cease-fire should be attained as a condition to launching a dialogue between Kyiv and representatives of protesters in southeast Ukraine."
Russian President Vladimir Putin said on June 22 that he supports Poroshenko's call for a cease-fire but said a cessation of hostilities is meaningless without a dialogue between the opposing parties.