"It is just a punitive operation and it will of course incur consequences for the people making these decisions, including (an effect) on our interstate relations," Putin said in a televised meeting with regional media.
Reuters journalists saw a Ukrainian detachment with five armoured personnel carriers take over a checkpoint on a road north of Slaviansk in the late morning after it was abandoned by separatists who set tyres alight to cover their retreat.
However, two hours later the troops pulled back and it was unclear if Kiev would risk storming Slaviansk, a city of 130,000 that has become the military stronghold of a movement seeking annexation by Moscow of the industrialised eastern Ukraine.
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"Finish what we have started"
At another checkpoint set up by the Ukrainian military, a soldier said they were there to instil law and order.
"Those separatists, they violated the constitution, they are torturing the country, they violated laws, they do not recognise the authority of police so the army had to move in and we will finish what we have started so help me God," he said.
The Geneva agreement, signed by Russia, the United States, Ukraine and the European Union, was already in trouble as Kiev launched its offensive to regain control of the east.
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East and West have put the onus on each other to ensure the accord is implemented on the ground. U.S. President Barack Obama said earlier he was poised to impose new sanctions on Moscow if it did not act fast to end the armed stand-off.
Putin said sanctions were "dishonourable" and destroyed the global economy but that so far the damage had not been critical.
Russia's Defence Minister said it had begun military drills near the border with Ukraine, where it has deployed tens of thousands of troops, in response to "Ukraine's military machine" and NATO exercises in eastern Europe.
Moscow also flexed its economic muscles in its worst stand-off with the West since the Cold War, with the government suggesting foreign firms which pull out of the country may not be able to get back in, and a source at Gazprom saying the gas exporter had slapped an additional $11.4 billion (6.7 billion pounds) bill on Kiev.
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Washington accuses Moscow of fomenting unrest in the east. Russia denies this and counters that Europe and the United States are supporting an illegitimate government in Kiev.
Obama said the Russian leadership was not abiding by the spirit or the letter of the Geneva agreement so far.
"We have prepared for the possibility of applying additional sanctions," he told a news conference on a visit to Japan. "There's always the possibility that Russia, tomorrow, or the next day, reverses its course and takes a different approach."
U.S. troops arrive in Poland
So far, the United States and EU have imposed visa bans and asset freezes on a few Russians in protest at Moscow's annexation last month of Crimea from Ukraine.
In NATO member Poland, the first group of a contingent of around 600 U.S. soldiers arrived on Wednesday. They are part of an effort by Washington to reassure eastern European allies who are worried by the Russian build-up near Ukraine's borders.
Acting Ukrainian President Oleksander Turchinov called for the eastern offensive on Tuesday after the apparent torture and murder of a member of his own party from Slaviansk.
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A local opposition activist called on the police to clear up the death of Volodymyr Rybak, a member of the Batkivshchyna party who had remained loyal to Kiev.
"He was bruised and punctured from head to toe ... it's clear they tortured him," said Aleksander Yaroshenko, a family friend who accompanied Rybak's widow when she identified his body at the morgue. "The police have lots of details, they have CCTV footage, they should know who did this," he told Reuters.
The government said the city hall in another eastern town, Mariupol, which had been seized by separatists, was now back under central control. Interior Minister Arsen Avakov said the mayor was back in his office.
Kiev also reported a shootout overnight in another part of the east when a Ukrainian soldier was wounded, while pro-Russian separatists in Slaviansk were holding three journalists, including U.S. citizen Simon Ostrovsky. [Update: Ostrovsky, a journalist with Vice News, told Reuters Thursday afternoon that he had been released in good condition.]
Ukraine, a former Soviet republic, slid into unrest late last year when Moscow-backed President Viktor Yanukovich rejected a pact to build closer ties with Europe. Protesters took over central Kiev and he fled in February.
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Days later, Russian troops seized control of Crimea. Moscow then annexed the region, saying it was protecting Russian residents, while the West called the action a land grab.
The focus has now shifted to eastern Ukraine, the industrial heartland and home to a large Russian-speaking community.
No way back?
With rhetoric building from the United States about the imposition of a new, tougher round of sanctions, Russia suggested on Thursday that Western firms which pulled out of the country may not be able to get back in.
"It is obvious that they won't return in the near future if they sever investment agreements with us," Natural Resources Minister Sergei Donskoy told reporters.
"Russia is one of the most promising countries in terms of hydrocarbons production. If some contracts are severed here, then, colleagues, you lose a serious lump of your future pie," the minister added.
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However, Western oil majors BP and Royal Dutch Shell were sticking with their projects in Russia, he noted.
Supplies of Russian gas to Europe are also, potentially, at risk from the crisis over Ukraine. Moscow has threatened to cut Kiev off unless it pays off its debts, and drastically raised this bill this week.
State-controlled Gazprom sent Ukrainian energy firm Naftogaz an additional bill on Wednesday of $11.4 billion (6.7 billion pounds), more than five times its previous claim, a source at the company said. This was in addition to the $2.2 billion (1.3 billion pounds) that Naftogaz already owes for supplies in 2013 and 2014 so far.
Moscow nearly doubled the gas price for Ukraine from April but Kiev, which is in financial trouble, is refusing to pay.
If Moscow cuts off the flow to Kiev, this would have a knock-on effect on European customers further West, because many of the pipelines that deliver their gas run through Ukraine.
European and Ukrainian officials were to meet in Slovakia, which borders Ukraine, on Thursday to try to work out ways to mitigate the impact if Ukraine is cut off.
The options include reversing the usual east-west flow of the pipelines to Europe to pump gas back into Ukraine, but the volumes that could be supplied this way would be only a small fraction of the amount that Ukraine needs.
Unarmed mediators from the Organisation for Security and Cooperation in Europe are in eastern Ukraine trying to persuade pro-Russian gunmen to go home, in line with the Geneva accord.
Reuters reporters have not been able to establish that any Russian troops or special forces membersare in the region, though Kiev and Western powers say they have growing evidence that Moscow has a covert presence.
Putin has described as "nonsense" allegations that Moscow has its forces in eastern Ukraine. It says the unrest is a spontaneous protest by local people who fear persecution from the government in Kiev which it says is illegitimate and has far-right links.