National Security and Defence Council chief Andriy Parubiy said the armed forces would expand the "active stage of the operation in other towns where extremists and terrorists are carrying out illegal activities".
AFP reporters near the eastern town of Kostyantynivka, where rebels seized the town hall on April 28, saw a pro-Russian checkpoint abandoned and smouldering while barricades were being hastily erected in the centre.
Rebels defending the town hall behind makeshift barriers told AFP there had been fighting overnight near the town's television tower.
In nearby Kramatorsk, pro-Russians were holed up in the town hall and burned-out trolley buses and minivans blocked off streets in the city centre.
On Saturday, fierce gun battles erupted around the flashpoint town of Slavyansk as the army stormed rebel-held checkpoints, tightening the noose around what has become the epicentre of pro-Russian fervour.
Central Slayvansk was relatively calm early Sunday but citizens reported increasing difficulty obtaining basic foodstuffs in the besieged town of 1,60,000 people.
Meanwhile, seven European inspectors from the Organisation for Security and Cooperation in Europe arrived home late Saturday after an eight-day ordeal in rebel captivity, a small chink of light in the worst East-West crisis since the Cold War.
Interim president Oleksandr Turchynov declared two days of mourning Saturday after brutal violence in Odessa claimed 42 lives and at least 10 died in military operations around Slavyansk, the worst bloodshed in months.
The scenic Black Sea port of Odessa was bracing for fresh unrest as supporters of the Western-backed government in Kiev planned a new march amid fears it could be disrupted by pro-Russian militants.
The city was still reeling from horrific violence on Friday when deadly clashes between the two sides culminated in a building fire that left 38 dead, most overcome by fumes, others from jumping from windows in a desperate bid for survival.
Four others died from gunshot wounds as the violence that has gripped the eastern part of Ukraine spread to the south, which had until then had been spared.
Prime Minister Arseniy Yatsenyuk visited the town on Sunday and told the BBC he would launch a "full, comprehensive and independent investigation" into the bloodshed, blaming "inefficient" local law enforcement officers.
Sporadic fighting was also reported overnight in the eastern city of Lugansk and the port city of Mariupol.
Meanwhile in Crimea, annexed by Russia in March, there were clashes between police and 2,000 pro-Kiev Tatars demonstrating against Russia's refusal to allow their leader Mustafa Dzhemilev into the peninsula.
Ukraine's violence sparked a new round of accusations and counter-accusations between the United States and Moscow as relations between the Cold War foes continued to suffer.
Russian Foreign Minister Sergei Lavrov called his US counterpart John Kerry to demand Washington use its influence over Kiev to stop what he called Ukraine's "war against its own people".
Lavrov warned that the military operations were pushing the former Soviet Republic towards a "fratricidal conflict" and urged a greater mediating role for the OSCE.
Moscow has warned that holding a planned presidential election on May 25 would be "absurd" amid the violence rocking the country.
This opened up the possibility that the West could impose its toughest sanctions yet on Russia, after US President Barack Obama said he would step up economic action against Moscow if it destabilised its neighbour ahead of elections.
Kerry stressed to Lavrov the "possibility or the reality of sectoral sanctions" targeting specific areas of the already weakening Russian economy.
He hailed the release of the OSCE inspectors -- secured after Russian President Vladimir Putin sent a special envoy to the region -- as a welcome step but stressed others needed to be taken "in order to be able to de-escalate the situation".
The Kremlin has pronounced dead an accord struck last month in Geneva to defuse the crisis.
It said it had received "thousands of calls" from eastern Ukraine requesting "active help".
Russia has an estimated 40,000 troops on the border that Putin has said he "hopes" not to have to use. In response, Ukraine has reintroduced conscription and placed its army on "full combat alert".
As Moscow and Washington traded barbs about interference in Ukraine, Germany's Bild daily alleged that dozens of US intelligence agents were advising the Kiev authorities, citing unnamed Germany security sources.
Arriving home in Berlin, the German leader of the seven OSCE captives voiced his relief after eight days in detention at the hands of insurgents in Slavyansk.
"Imagine, last night we were in the midst of gunfire, tonight we are with our families. We would never have thought it possible," Colonel Axel Schneider told reporters at Berlin airport.
One of the Czech observers, Lieutenant Colonel Josef Prerovsky, told reporters they had spent the first hours of their captivity in a basement blindfolded and with their hands tied.
"We spent the first two days in a basement constantly under guard, accompanied even when we went to the bathroom," he said.
Authorities in Kiev and the West blame Russia for fomenting the chaos in eastern Ukraine, where separatists have vowed to hold an independence referendum on May 11.
Russia denies the charges but has vowed to respond if its interests in Ukraine are threatened.