Ukrainian government forces have advanced on several eastern towns amid heightened tension after the fatal clashes of recent days.
Latest reports say pro-Russian rebels attacked a Ukrainian military unit at Luhansk, wounding two soldiers.
Armed separatists have been reinforcing barricades in the town. The number of demonstrators is said to have increased dramatically.
Earlier, at Kramatorsk, the security service headquarters and TV tower were recaptured from rebels by the National Guard on Saturday.
Health authorities said at least six people were killed in fighting. Russian state media reported a higher number of casualties but there has been no independent confirmation.
The army are said to have destroyed pro-Russian rebel checkpoints as they focus on smaller towns where separatists have been in control of government buildings.
The larger town of Slovyansk remains surrounded, with residents said to be fearful of an all-out government assault.
Pro-Russian protesters in Donetsk stormed the state security headquarters and the regional governor’s business premises.
Demonstrators chanted “we won’t forget Odessa” following Friday’s fatal violence in the southern port city. At least 46 people were reported killed in clashes between pro-Kyiv and pro-Russian demonstrators.
The EU has called for an independent inquiry into the violence and for those responsible to be brought to justice.
Russia’s Foreign Minister Sergei Lavrov has told his US counterpart John Kerry that the US should use its influence to make Ukraine’s government immediately stop military operations in south-east Ukraine, the Russian foreign ministry said in a statement on Saturday.
Lavrov also said that it was important that the mediating role of the Organization for Security and Co-operation in Europe (OSCE) was increased to secure Kyiv’s fulfilment of the Geneva declaration on de-escalating tensions in Ukraine.
Washington again said Moscow should stop backing pro-Russian separatists. Kerry warned that Russia risked incurring further sanctions.