The clashes were the first since acting President Oleksandr Turchynov ordered the resumption Tuesday of military operations in eastern Ukraine, where pro-Russia protesters and masked gunmen have seized government buildings in at least 10 cities and set up roadblocks.
In St. Petersburg, Russian President Vladimir Putin decried what he described as Ukraine's "punitive operation" and threatened Kiev with unspecified consequences.
"If the Kiev government is using the army against its own people this is clearly a grave crime," Putin said.
Later in the day, Russian Defense Minister Sergei Shoigu announced new military exercises in Russia's south and west in reaction to the mounting unrest in eastern Ukraine and NATO exercises in Poland.
"We have to react to these developments somehow," he said in televised comments.
Russia already has tens of thousands of troops stationed in regions along its border with Ukraine. The latest Russian military exercises will involve ground troops in the south and the west and the air forces patrolling the border, Shoigu said.
He also quoted unspecified sources saying that Kiev has deployed more than 11,000 troops and 160 tanks against the pro-Russia insurgents which he put at less than 2,000 troops. There was no way to immediately verify those figures.
The Ukrainian government and the West have accused Russia of directing and supporting the insurgents and worry that Putin would welcome a pretext for a military intervention in eastern Ukraine. Putin denies that any Russian agents are operating in Ukraine, but insists he has the right to intervene to protect the ethnic Russians who make up a sizeable minority in eastern Ukraine.
Earlier in Tokyo, President Barack Obama accused Moscow of failing to live up to "the spirit or the letter" of a deal last week to ease tensions in eastern Ukraine. If that continues, Obama said, "there will be further consequences and we will ramp up further sanctions."
With no appetite in the U.S. for a military response, Obama is largely banking on Putin caving under a cascade of economic sanctions targeting his closest associates. But the success of that strategy also depends on European nations with closer financial ties to Moscow taking similar action, despite their concern about a boomerang effect on their own economies.
"I understand that additional sanctions may not change Mr. Putin's calculus," Obama said on a Tokyo visit. "How well they change his calculus in part depends on not only us applying sanctions but also the cooperation of other countries."
The Ukrainian Interior Ministry said military and special police forces killed "up to five terrorists" while destroying three checkpoints north of Slovyansk, a city 160 kilometers (100 miles) west of the Russian border that has emerged as the focus of the armed insurgency. One government member was injured, the statement said.
Stella Khorosheva, a spokeswoman for the Slovyansk insurgents, said two pro-Russia fighters were killed at a checkpoint in the village of Khrestyshche, 10 kilometers (six miles) north of the city. She said checks were being made at hospitals to see if there were other casualties.
The situation was quiet in Slovyansk itself, but checkpoints inside the city were abandoned and it was unclear where the pro-Russia insurgents manning them had gone.
Khorosheva later said the pro-Russian militia had regained control over the disputed checkpoints and the fighters were ready to repel any attack by government troops.
"We will defend ourselves to our last drop of blood. We are ready to repeat Stalingrad," she told The Associated Press, invoking the memory of the Soviet army's victory over German forces in 1942-43.
At least 10 Ukrainian government armored vehicles were seen on the road north of Slovyansk and two helicopters were circling over the area. Troops ordered residents in the area to keep away.
Near the town of Makatikha, several miles (kilometers) north of Slovyansk, pro-Russia militia set fire to barricades of car tires in an apparent attempt to reduce the visibility from the air. An Associated Press reporter saw about two dozen militiamen manning checkpoints along the road earlier in the day.
In the southeastern city of Mariupol, Interior Minister Arsen Avakov said his forces had cleared city hall of the pro-Russia protesters who had been occupying it for more than a week. He did not describe the operation. The Ukrainian city sits along the main road between Russia and Russia's newly annexed Black Sea peninsula of Crimea.
Yulia Lasazan, a spokeswoman for Mariupol's police department, told The Associated Press about 30 masked men armed with baseball bats stormed the building in the dark early Thursday and started beating the protesters. Five people were taken to a hospital, she said.
It was not clear why the protesters, some of whom were believed to be armed, did not offer resistance but called local police instead. Lasazan said the police were controlling Mariupol city hall's perimeter and were negotiating with the remaining protesters to leave.
Ukraine is going through its biggest political crisis since the fall of Soviet Union, set off by months of anti-government protests that led to President Viktor Yanukovych's flight to Russia in February.
Yanukovych's ouster sparked wide anger in his support base in Ukraine's east. The insurgents, who claim Ukraine's post-Yanukovych government consists of nationalists who will suppress the east, are demanding regional autonomy or even annexation by Russia.
Ukraine and Russia reached a deal in Geneva last week to defuse the crisis, but pro-Russian insurgents in the east - and right-wing militants in Kiev - have defied calls for all sides to disarm and to vacate the buildings they are occupying.