Ukrainian President Petro Poroshenko ordered military forces Sunday to "tighten the ring around the terrorists," a day after the country's troops recaptured Slovyansk from pro-Russian separatists.
Ukraine's government said it would seize more territory from rebels in what Poroshenko called a turning point in the fight for control of the country's east.
Government forces routed pro-Russian rebels in the flashpoint city on Saturday and raised the blue and yellow national flag over what had for months been a separatist redoubt. The seizure appeared to dim hopes for a cease-fire in the fighting.
On Sunday, Ukrainian forces shelled parts of the rebel-held town of Luhansk near the Russian border, hitting a battery-making factory and other buildings, Russia's Itar-Tass news agency reported, quoting rebels in the town.
The government said some people were wounded but there was no further word on casualties.
However, the rebels admitted suffering heavy losses and abandoned the strategic city nearly three months to the day after its capture marked the onset of a new and even bloodier chapter in Ukraine's worst crisis since independence in 1991.
"My order is now in effect - tighten the ring around the terrorists," Poroshenko tweeted on Sunday.
"Continue the operation to liberate Donetsk and Luhansk regions," he said, naming Ukraine's two major eastern parts that have boiled with separatist rebellion since April.
In a statement, Ukraine Interior Minister Arsen Avakov said: "We have a plan of action. … We will move forward every day."
The government offensive in Slovyansk came after Poroshenko refused to renew a unilateral cease-fire and ordered the resumption of a government offensive on June 30.
Most analysts think Poroshenko needed a battlefield success one month into his presidency to secure the trust of Ukrainians frustrated by their underfunded army's inability to stand up to what they see as Russian aggression, the French news agency AFP reported.
Ukrainian forces said they now had full control of Slovyansk and the nearby town of Kramatorsk.
Many rebels appeared to have retreated toward Donetsk, the east's main industrial hub where separatists first declared a "people's republic."
Armed rebels were patrolling one of the main streets of Donetsk on Sunday, local news agency Novosti Donbass said.
"Winning the battle is not the same as winning the war," said one rebel gunman manning a checkpoint outside the city to the Associated Press. "Let them try to come to Donetsk. Then we'll see. War is just starting."
Slovyansk has been the most important stronghold of the militants fighting government forces in mainly Russian-speaking eastern Ukraine, a focal point of tensions between the West and Russia.
The town's re-capture represents Kyiv's most notable military victory in three months of fighting in which more than 200 Ukrainian troops have been killed as well as hundreds of civilians and rebels.
"This is not full victory. But the clearing out of people armed to the teeth from Slovyansk has huge symbolic importance. It is the beginning of the turning point in the battle with fighters for the territorial integrity of Ukraine," said Poroshenko.
He said hostages held there by the separatists had been released and a significant number of weapons had been seized.
But he warned that the rebels were re-grouping in other big towns and he said he was far from euphoric.
"There are further tests ahead," he said.
Ukrainian forces on Sunday reported recapturing four small cities straddling the road between Slovyansk and Donetsk.
"Yes, we are losing a lot, but I am sure that our defense of Donetsk will mark a turning point," Donetsk rebel leader Denis Pushilin confirmed in a tweet. "We will win."
However, newly appointed Defense Minister Valery Heletey vowed rebels who do not quit fighting will be killed.
"In the coming days, I believe, you will become witnesses that those people who refuse to lay down arms, who do not understand that fighting against Ukrainian army and Ukrainian people is not just dangerous will realize that it will be a sentence for them,'' Heletey said.
And many in Slovyansk seemed relieved to see the gunmen finally leave their shelled-out city's streets.
"We felt like hostages," a retired teacher named Anna Gribnikova said a few steps away from a line of several hundred people patiently waiting for bread handed out by Ukrainian relief staff.
Andriy Lysenko, a senior official of Ukraine's "anti-terrorist operation," said: "The bands of terrorists are demoralized, but they are all the same carrying out treacherous attacks on Ukrainian forces."
In Slovyansk and neighboring areas, he said, scores of rebels were surrendering.
"Those who are giving themselves up are providing information about units of (rebel) fighters and where weapons are," Lysenko said.
Moscow, which has already come under economic sanctions from the West, denies Western and Kyiv's accusations it has been backing the insurrection possibly with a view to dismembering the former Soviet republic.
The uprisings in eastern Ukraine erupted in April as rebels took over state buildings, built a powerful arsenal of seized weapons and declared their independence from Kyiv, calling the pro-European government illegitimate.
The crisis began when street protests ousted Moscow-backed Viktor Yanukovych in late February for rejecting a landmark political and trade deal with the European Union in favor of closer ties with Russia.
Russia subsequently annexed Crimea and separatist revolts against the new Kyiv authorities broke out with rebels, widely believed to be supported by Moscow, declaring "people's republics" and saying they wanted to join Russia.
Talks in Berlin last week involving the foreign ministers of Ukraine, Russia, Germany and France had set Saturday as the day for talks between a contact group representing Ukraine, Russia and the OSCE security watchdog, and separatist leaders.
The talks were to have been aimed at working out an effective cease-fire observed by the opposing sides, but against the background of the military action in Slovyansk there was no sign they had actually been held.
Poroshenko declared a week-long unilateral cease-fire on June 20 which he renewed for a further three days.
But he refused last Monday to extend it any further, citing unceasing rebel attacks that killed more than 20 soldiers and - according to both Washington and Kyiv - allowed the separatists to stock up on new supplies of heavy Russian arms.
Poroshenko then sent government forces into an offensive against the rebels.
Russia has denied allegations by Kyiv that it has been fanning the separatist rebellions by allowing weapons and fighters to cross over the long joint border to support the separatists.
It has been pressing Poroshenko to engage in talks with the separatists and agree on a cease-fire.
Some information for this report provided by Reuters, AFP and AP.