* Threat of Russian invasion hangs over east Ukraine
* Putin seen more likely to stir dissent than send in troops
* Russians glad to win back Crimea but most don't want war
By Steve Gutterman
MOSCOW, March 17 (Reuters) - As Russian forces took control of Crimea in the last few weeks, Russian media started referring to a broad belt of land in southern Ukraine as Novorossiya, or New Russia.
The revival of the Tsarist-era name plays well with Russian voters and harks back to a remark in 2008 when President Vladimir Putin told NATO leaders the area contained "only Russians". Six years on, Ukrainians are worried that comment is starting to look prophetic.
With Russia's armed forces holding war games near the border and Moscow threatening to intervene to halt violence against Russians in Ukraine, some fear Putin will not stop at Crimea and may try to grab more territory in the east and south.
Some Russians dream of annexing most of eastern and southern Ukraine, cutting the country in half and extending Moscow's reach to the border of Transnistria, a breakaway sliver of Moldova that has strong Russian ties.
"It's clear that the Kremlin's actions ... will be aimed at acquiring this whole piece of land up to Transnistria - and, of course, the eastern regions (of Ukraine)," Russian political commentator Yulia Latynina said on Ekho Moskvy radio.
Doing so would dramatically raise the stakes in the biggest dispute between Russia and the West since the Cold War and increase the danger of direct military conflict.
But although such dreams have echoes of Serbian leader Slobodan Milosevic's vision of a Greater Serbia before the Balkan wars of the 1990s, many Western experts see such threats largely as posturing.
They suggest Putin may be trying to frighten the West into letting him keep Crimea, a Black Sea peninsula, in the hope that he will not press on with his ambitions.
"Putin would be mad to invade Ukraine," one Western official said, adding that he would be more likely to decide on "playing it long, fomenting rebellion among the ethnic Russians" in the long-term hope of winning control of territory without a fight.
The Eurasia Group, a U.S.-based think tank, said that "a Russian invasion remains very possible but on balance unlikely".
"Moscow will continue to seek more influence primarily by destabilising eastern Ukraine," it said.
Russia's plans for eastern Ukraine remain hard to predict but even if few people in the West believe a military conflict is likely, almost no one seems to rule it out.
FAST MOVES IN CRIMEA
Moscow has moved fast to bring Crimea into the fold after Ukraine's Moscow-backed president, Viktor Yanukovich, fled Kiev on Feb. 21 after signing a deal with his opponents intended to end three months of anti-government protests.
Yanukovich had set off the protests with his decision in November to spurn political and trade deals with the European Union and instead seek closer ties with Moscow.
After such a bitter defeat for Putin, a chance of gaining something out of the crisis emerged in Crimea, where Russia's Black Sea fleet is based.
Russian forces bloodlessly took over military bases and pro-Russia forces took charge of the region's parliament and government. Russia said the armed groups, without any insignia, were not sent by Moscow - a statement ridiculed in the West.
On Sunday the southern peninsula, which has an ethnic Russian majority, voted for union with Russia.
Frequent violence in eastern Ukraine, involving pro-Russians and groups loyal to the new Kiev authorities, raises the prospect of Russian forces moving into eastern and southern regions.
Kiev says Russia is deliberately trying to incite violence to create an excuse to invade. Moscow denies this.
On March 1, Putin secured permission from his parliament to send the military into Ukraine to protect Russians if needed. He has put forces near the border on alert twice in recent weeks for sabre-rattling military drills.
After meeting U.S. Secretary of State John Kerry on Friday, Foreign Minister Sergei Lavrov assured the world Russia "does not and cannot have any plans to invade the southeastern regions of Ukraine", but added that only the staunch resolve of armed units in Crimea had prevented bloodshed there.
Putin kept the implicit threat of invasion alive in telephone talks with U.S. President Barack Obama on Sunday, saying Russia was concerned by what he called "rampant violence by ultra-nationalist and radical groups that destabilise the situation and terrorise civilians".
RUSSIA MEDIA WHIP UP HOSTILITY
Russian state media have beamed similarly dire depictions into the homes of millions of Russians, portraying Ukraine as a chaotic and violent state on the verge of collapse and suggesting Russian-speakers are living under constant threat of attack by the "neo-fascists" they say have taken control in Kiev.
"The country is falling apart at the seams," presenter Dmitry Kiselyov, who was awarded a medal by Putin last month for "service to the fatherland", said on his weekly show on Sunday.
Plenty of Russian politicians, both inside and outside Putin's camp, say Moscow is ready to rescue Russians in Ukraine - and anyone there who feels impoverished or downtrodden.
Communist Party leader Gennady Zyuganov said the Crimean referendum should be "an example for many regions of Ukraine which are now in a distressed and difficult situation".
Vera Goloshchapova, a 60-year-old pensioner in the southeastern Ukrainian coal mining city of Donetsk, needs no referendum. She would welcome a Russian invasion now.
"Ukraine has abandoned us," she said, blaming violence in the city on nationalists from western Ukraine whom she associates with militants she said killed her relatives during World War Two. "I have no motherland - it's been ripped to shreds. Let Putin send in forces."
Even if Western governments were to accept Russia's claim of a threat to its citizens in eastern Ukraine, however, sending in troops would be highly risky for Putin.
"Are we really going to kill each other? I can't get my head around it," said Lyudmila Tsymbalyuk, 50, a nurse in Donetsk. "I don't want to be in Russia. Nobody is oppressing me here."
At home, Putin's popularity has shot up amid strong support for bringing Crimea into Russia. But polls show few people in Russia want war, and some would see sending in troops as an act of aggression against what he has called a "brother nation".
"In ... Crimea it was all done well. There was no violence," Russian pensioner Vera Zatsevina, 59, said outside the GUM department store on Moscow's Red Square. "Now, though, it looks like it is western Ukraine versus eastern Ukraine and I am worried about a war. It's better when things are peaceful."
There is a danger of the confrontation rising to a new level, increasing the wrath of the United States and Europe and leading to further sanctions in addition to those set out by Brussels and Washington on Monday.
Many Russians welcome what they regard as Crimea's return, which could be approved by Russian parliament within a few days.
The region was transferred from Russia to Ukraine in 1954 by Soviet leader Nikita Khrushchev, apparently on a whim. This had rankled ever since.
Suggesting Russia wanted to grab more territory, Andriy Paruby, Secretary of Ukraine's National Security and Defence Council, said a Russian plot had been foiled to seize control of eight other regional government headquarters.
"Russia is trying to send trained and armed saboteurs" into Ukraine, Paruby said, but he added that the authorities were detaining hundreds of them every day. "Despite the efforts of Kremlin strategists, we are managing to keep the situation in the southern and eastern regions under control," he said.
Putin could, however, settle for less then full secession or annexation of mainly Russian-speaking regions in Ukraine, the cradle of Russian civilisation and regarded by many Russians as little more than their country's vassal.
Russia could use discord in the east and south to press for a new constitution that would give Ukraine's regions broad powers - part of a plan, analysts say, to keep the nation formally intact while corroding its unity, breaking it apart in practice and gaining as much influence as possible.
Still, Putin has already rewritten Russia's foreign policy playbook, and few believe an invasion can be ruled out.
The Eurasia Group put the probability that Russia would invade eastern Ukraine at 40 percent. As the Western official put it: "Putin may decide to go for the jugular quickly."
In Donetsk, that was the fear of the nurse, Tsymbalyuk. "Putin has lost his mind," she said. "He has the nuclear button, there are tanks at the border. Crimea is already under Russia, tomorrow will it be Donetsk?" (Additional reporting by Lina Kushch in Donetsk, Natalia Zinets in Kiev, Ian Bateson in Moscow and Peter Apps in London; Editing by Timothy Heritage and David Stamp)