Pro-Russian militants just outside Sloviansk have retreated amid attacks by Ukrainian troops, reports say.
Government forces took control of a TV tower in the suburbs and rebels were pulled back deeper into the city, the Russian Interfax news agency said.
Earlier reports told of heavy gunfire, apparently closer to the centre than in recent days.
Meanwhile, militants shot down a military helicopter near Sloviansk, the defence ministry said in a statement.
The crew of the aircraft survived, largely because the helicopter crashed into a river, the ministry added. It was the third Ukrainian military helicopter to be downed over the city in recent days.
A BBC team which has reached the centre of Sloviansk says there has been a lull in the fighting between about 800 pro-Russian militants and Ukrainian troops.
Local residents reported heavy gunfire on Monday morning, but only isolated shooting can still be heard.
Four Ukrainian soldiers were killed and 30 injured during the fighting in Sloviansk, the interior ministry said.
Fears of an impending offensive by Ukrainian forces on the pro-Russian stronghold had been growing overnight, sources inside the city said earlier.
Ukraine’s army cut off the main road into the city on Sunday.
The move came days after rebels shot down two Ukrainian helicopters on the outskirts of Sloviansk, one of a dozen or more east Ukrainian cities where pro-Russian separatists have seized official buildings.
Ukrainian troops are currently carrying out what the Kiev government calls “anti-terror” operations in the east to wrest back control of these areas.
Speaking two days after dozens were killed in violence in the southern Ukrainian port city of Odessa, Prime Minister Arseniy Yatsenyuk accused Russia of executing a plan “to destroy Ukraine and its statehood.”
“Russia’s aim was to repeat in Odessa what is happening in the east of the country,” he said, insisting Kiev had not lost control of the region.
The clashes on Friday left more than 40 dead, mostly pro-Russian separatists killed in a building fire.
Russia warned on Monday that failure to halt the escalating unrest would threaten peace across Europe.
Moscow called on Ukraine and the international community to step up “joint efforts” to end “racism, xenophobia, ethnic intolerance, (and) the glorification of the Nazis” - a reference to extremists Russia claims are committing “mass” rights violations in Ukraine.
“The alternative is fraught with such destructive consequences for Europe’s peace, stability and democratic development that it is absolutely necessary to prevent it,” the Russian foreign ministry said in a statement.