But the Ukrainian defence ministry says six armoured personnel carriers were captured by pro-Russian militants.
Other reports suggest the Ukrainian troops may have abandoned their vehicles or changed sides.
Tension is increasing across eastern Ukraine where pro-Russian protesters have seized public buildings.
The crisis escalated this month after pro-Russian rebels occupied buildings in about 10 towns and cities, demanding greater autonomy or referendums on secession.
In the city of Donetsk, which has seen weeks of unrest, pro-Russian gunmen have taken control of the mayor's office.
Tens of thousands of Russian soldiers are believed to have massed on Ukraine's borders since Russia took control of the Ukrainian region of Crimea last month, following a controversial referendum on self-determination.
Continue reading the main story Olga Ivshina BBC Russian Service, KramatorskPeople are very nervous. Many have not slept for several nights. When Ukrainian armoured personnel carriers appeared in the town, people quickly surrounded them. Some accused soldiers of "acting against their own people."
"Why did you come to our land?" a man from the crowd asked. "Why are you driving over our fields? We are peaceful people! And we just want our demands to be respected!"
Soldiers were sitting on the APCs with automatic guns, in full combat gear. "I know they can shoot at us, but we are miners, we see death every day," the man said. "So we are not afraid. We will stand here until victory. We want a referendum to be held. We should decide our future for ourselves."
"We are just obeying orders, let us go!" the commander shouted. "We didn't come here to fight. We are just moving around. I will never shoot at my own people!"
As tensions rose, Ukraine's acting Defence Minister Mykhailo Koval headed for the east of the country to monitor the progress of the "anti-terrorist operation" announced by acting President Olexander Turchynov on Tuesday.The interim Prime Minister, Arseniy Yatsenyuk, called on Russia to "stop supporting terrorists in Ukraine".
'Not to fight'After Ukrainian forces recaptured an airfield outside Kramatorsk on Tuesday, armoured vehicles appeared in the centre of the town early on Wednesday.
BBC journalists witnessed civilians, at least some of whom appeared to be local people, challenging soldiers, who were also blocked by a crowd a few kilometres outside the town.
One officer said he had not "come to fight" and would never obey orders to shoot his "own people".
Video later emerged of six armoured personnel carriers, flying Russian flags, entering the nearby town of Sloviansk.
Villagers have confronted Ukrainian soldiers in the villages of Novoselivka and Ivanivka near KramatorskIn a statement on its Facebook page, the Ukrainian defence ministry maintained they were taken there by "extremists" and that Russian secret service agents were involved in their seizure in Kramatorsk.
A soldier guarding one of the carriers told Reuters he was a member of Ukraine's 25th airborne brigade from Dnipropetrovsk, a city also in eastern Ukraine.
He said the soldiers had had no food for four days until local people fed them.
"All the soldiers and the officers are here," he said. "We are all boys who won't shoot our own people."
In Donetsk, where activists have been occupying the regional government building since 6 April, gunmen met no resistance as they entered the mayor's office.
They told an AFP correspondent their only demand was for the region to stage a referendum on turning Ukraine into a federation with broader local rights.
Gunmen inside the mayor's office in Donetsk 
Ukrainian soldiers watching a jet pass near Kramatorsk 
A column of armour flying a Russian flag near Kramatorsk 
Women stand near soldiers wearing pro-Russian ribbons in Sloviansk Russia accused Meanwhile Nato announced it was beefing up its eastern members' defences.
In Brussels, Nato Secretary General Anders Fogh Rasmussen promised "more planes in the air, mores ships on the water, more readiness on the land".
He called on Russia to make clear it did not "support the violent actions of well-armed militias or pro-Russian separatists in eastern Ukraine".
Continue reading the main story
Jonathan Marcus BBC diplomatic correspondent Nato's announcement is about reassuring worried allies in the Baltic Republics and central Europe as well as signalling to Moscow that when it comes to the alliance's core business - the defence of its members' territory - Nato is as vigilant as ever.
Air patrols over the Baltic republics are to be stepped up; Nato warships will deploy to the eastern Mediterranean and the Baltic Sea.
And on land staff officers will be despatched to oversee an enhanced programme of exercises and preparedness in the countries most concerned.
Nato will also review and reinforce its defence plans. In the longer term additional deployments may well be made, Nato sources indicating that this is only the first step of several that could be taken if the relationship with Russia sours further.
The Nato alliance includes two ex-Soviet Baltic republics with large ethnic Russian communities, Latvia and Estonia, while other members such as Poland share borders with Russia.Four-way talks are due to take place on Thursday in Geneva between diplomats from Russia, the EU, the US and Ukraine.
Ukrainian and Western officials have accused Russia of being behind the pro-Russia activism in the region while Moscow denies fomenting the unrest.
Ahead of the annexation of Crimea, masked soldiers believed to be Russian troops appeared at strategic points across the peninsula alongside "self-defence" units, said to have been formed locally.
Speaking in London, UK Foreign Secretary William Hague said Russia had sent "thinly disguised" armed groups into eastern Ukraine to spearhead the occupation of buildings.
Ukraine's Security Service (SBU) has meanwhile published what it says is a batch of intercepted conversations between the Russian secret services and pro-Russian forces in eastern Ukraine.
Russian security service officers are heard to order forces in eastern Ukraine to "shoot to kill" when dealing with Ukrainian troops who do not surrender, according to the transcripts.
Counter-intelligence spokesman Vitaliy Naida told reporters the same Russian agents had been involved in the run-up to Russia's Crimea annexation.
The intercepts could not be independently verified. Moscow maintains the pro-Russian protests in eastern Ukraine are the result of grassroots activism.
The US has said it is "seriously considering" adding to sanctions imposed after the annexation of Crimea. It described Ukraine's military operation as a "measured" response to a lawless insurgency.
Are you in eastern Ukraine? What is the situation like where you are? You can email your experiences to haveyoursay@bbc.co.uk using the subject line 'Eastern Ukraine'.
