* EU sets out its case for drawing in Ukraine, says offer remains
* History is not decided in days or weeks, says top EU official
* Message underlines Europe's battle of ideals with Russia
By Luke Baker
BRUSSELS, Feb 5 (Reuters) - If there is a consistent message the European Union has tried to send since Ukraine rejected a trade deal last November in favour of stronger ties with Moscow, it is that it does not want to end up in a tug-of-war with Russia.
But whether the EU likes it or not, that is precisely what has come to pass and the future of Ukraine - its 46 million people and its faltering economy - hangs in the balance.
In a speech to a security conference in Munich last weekend, European Council President Herman Van Rompuy laid out the nature of the struggle in simple terms.
The EU, he said, had offered Ukraine a free trade and association agreement to help it build bridges with its neighbours to the west. That offer still stood, as long as the conditions agreed between Kiev and Brussels were met.
"Some people think Europeans are naive, that we prefer carrots to sticks," Van Rompuy told the conference, whose delegates included Russian Foreign Minister Sergei Lavrov and a leader of Ukraine's opposition movement.
"Now I am not saying that we cannot sometimes play our hand more strongly. But surely it is a bad idea to let foul play undercut the very values that constitute our power of attraction in the first place - a power of attraction that brought down the Berlin Wall," he said.
"Our biggest carrot is our way of life; our biggest stick: a closed door."
The targets of Van Rompuy's words, without being named, were Russia's Vladimir Putin and Ukrainian President Viktor Yanukovich, who sparked the crisis by abruptly turning his back on an EU free trade deal and throwing his lot in with Moscow.
Yanukovich's security forces have cracked down on pro-EU demonstrators - at least five protesters have been killed - while Russia has enticed Kiev away from the EU with the promise of $15 billion in cheap loans and cut-price gas.
Some diplomats expected the EU to wash its hands and walk away. It cannot match Russia's inducements on either the financial or energy-security front. Instead, it appears to be playing a long game.
After EU foreign policy chief Catherine Ashton was quoted as saying Brussels and Washington were working on assistance for Kiev, EU officials were quick to say there was no new plan apart from the promise of financial help that Brussels had held out if it signed the trade agreement.
Even without the impact of the last four years of financial crisis, EU leaders are not about to open their coffers and disburse huge sums to Ukraine. It was hard enough to do so for Greece, Portugal and Ireland.
And, dependent on Russian energy themselves, EU member states cannot hope to provide Kiev with the gas it needs, especially as much of it flows to them via Ukraine.
What Europe has to offer is more conceptual: rule of law, democratic accountability, civil liberties and long-term trade and investment, as long as certain objectives are met.
Next to the sugar rush of money and cheap gas, it may not seem particularly attractive, especially given the costs Ukraine faces if it is ever to meet EU standards on judicial, industrial and environmental reform.
But as Van Rompuy pointed out, the course of history is not decided in a matter of weeks or months. The Berlin Wall may have collapsed almost overnight and the Soviet Union crumbled quickly, but those moments were years in the making.
"Sometimes in the heat of events, in the stream of declarations and tweets, we lose sight of the time factor," he told the Munich conference.
"We frantically look at hours and days, forgetting the years and decades. We lose sight of slow evolutions, of subtle trends. Subtler than the 'decline of the West' or the 'rise of the Rest'."
Moscow views Ukraine as a heartland of Russian culture and identity, a country that should never have left the Soviet Union. Russia remains Ukraine's biggest trading partner.
Putin wants Ukraine to join his Eurasian Union, a new economic and trade bloc he hopes will some day rival the EU. In that regard, he sees Brussels' overtures to Kiev as a threat.
In an arm-wrestle with the EU, Russia has the muscle. But in a long-run contest involving a way of life and integration with the global economy, the EU hopes it has a persuasive case - and one it says is not to the detriment of Russia.
"The offer is still there," Van Rompuy said of the agreement Yanukovich rejected last year. "We know time is on our side. The future of Ukraine belongs with the European Union." (Editing by Mike Peacock)