Separatist rebels have taken two Ukrainian military bases in the eastern region of Luhansk as fighting continues near the rebel-held town of Sloviansk.
Separatists seized a border guard base after days of fierce combat, and a National Guard base after an attack which began on Tuesday.
An apparent air attack in Luhansk city on Monday killed a number of civilians.
Meanwhile, in the neighbouring Donetsk region, troops are closing in on the rebel stronghold of Sloviansk.
Pro-Russian separatists in the Donetsk and Luhansk regions, Ukraine's industrial heartland, declared independence after holding referendums last month which were declared illegal by the government in Kiev.
The rebellion began amid the turmoil which followed the downfall in February of the elected Ukrainian President, Viktor Yanukovych, whose pro-Moscow policies sparked mass street protests in Kiev during the winter.
Reports of casualties in the fighting in Luhansk could not be verified independently.
Ukraine's border service announced on its website that the personnel in the base of the Luhansk border detachment had been "redeployed to safer places" as a result of sustained attacks by large rebel forces.
The National Guard base came under sustained fire from mortars, rocket-propelled grenades, machine-guns and assault rifles on Tuesday after the soldiers rejected an ultimatum from a large rebel force to surrender, according to a report on the National Guard's website.
Three soldiers were wounded and all of the base's vehicles and its headquarters building were destroyed in the fighting, the statement said. The garrison, it added, had now been "redeployed to a different, safe place".
However, a rebel spokesman told Russia's Ria-Novosti news agency the soldiers had surrendered and had been allowed to "go home".
The Russian news website ura.ru quoted a rebel commander as saying there had been "no battle as such" and the soldiers had simply surrendered after spiking some of their weapons.
Investigations are continuing into the attack on the rebel-held regional administrative building in Luhansk on Monday afternoon. Rebels have accused the Ukrainian air force of killing eight civilians in the attack, and graphic video of bodies at the scene has been posted on websites.
The Organization for Security and Co-operation in Europe said that, based on available evidence, "these strikes were the result of non-guided rockets shot from an aircraft. The number of casualties is unknown".
But the Ukrainian authorities deny their planes were involved and suggest the damage was caused by the rebels themselves.
Ukraine's interim President, Olexandr Turchynov, said in a statement on Tuesday that the northern part of Donetsk region had been "fully cleared" of separatists and the military had started blocking the border with Russia in the north and east of Luhansk region.
Government forces took the town of Krasnyi Lyman, north-east of Sloviansk, after heavy fighting.
A hospital was damaged by an air attack during the fighting and a surgeon killed by shrapnel, the hospital told Ukraine's Segodnya newspaper. Three patients were also wounded, it said. Photos of damage to the hospital were published by Segodnya.
The rebels told Ria-Novosti that eight of their fighters had been killed in the town.
In another development, Donetsk International Airport, scene of fierce fighting recently, said it would be closed until at least the end of June.
Russia has been accused of fomenting the rebellion, following its annexation of another Ukrainian territory, Crimea, in March.
Russian citizens have been fighting on the rebel side but President Vladimir Putin has again denied any official involvement by the Russian military. In an interview for French radio station Europe 1, he said: "No Russian military force and no Russian military instructor are present in south-east Ukraine".
Nato's top military commander, US General Philip Breedlove, has said that Russian irregular forces, and forces backed and funded by Russia, are very active in eastern Ukraine and "this has to stop".
Speaking in Brussels, he confirmed Russia was pulling back most of its troops from the Ukrainian border but a portion of the Russian force looked "like it intends to remain".