* Pro-Russian separatists control some border posts
* Ukraine is trying to take back control of frontier
* Oligarch proposes building a metal wall on border (Adds latest violence)
By Timothy Heritage
KIEV, June 17 (Reuters) - Ukraine's leaders are puzzling over how to cut off Russian support for a separatist rebellion in the east of the country but one of its richest men thinks he has the answer.
Billionaire businessman Ihor Kolomoisky has suggested building a wall along the almost 2,000 km (1,200-mile) land border with Russia to prevent fighters and weapons flooding in.
The idea may sound absurd but Kolomoisky has offered to stump up 100 million euros ($136 million) to fund the two-metre (six-feet) high, 25-30 cm (10-12 inch) thick wall of reinforced steel, complete with electronic alarms, trenches and minefields.
What's more, it's been done before. Israel has constructed a barrier to keep out Palestinian militants. China built the Great Wall to stop invaders. Soviet-led East Germany erected the Berlin Wall, though more to keep people in than out.
"We can take on this project from start to finish," said Alexei Burik, deputy head of the Dnipropetrovsk region where Kolomoisky is the governor, offering to lead construction work.
President Petro Poroshenko may or may not be about to build such a wall but the growing discussion of the oligarch's idea highlights deep security concerns in Ukraine, three months after Russia annexed the Black Sea peninsula of Crimea.
The Russian invasion of east Ukraine expected by many Ukrainians has not come. But in several weeks of fighting, pro-Russian separatists have seized a number of border posts, enabling them to bring in weapons and other supplies.
Securing the long and winding, and notoriously porous, border has become Poroshenko's most pressing problem as he tries to put down the rebellion and hold Ukraine together.
Fighting near the border has been among the fiercest of the conflict and 30 servicemen were wounded overnight in new clashes in Luhansk, a border guard command centre.
Kolomoisky, a 51-year-old banking, media, energy and metallurgy magnate with a fortune estimated by Forbes magazine at $1.8 billion, has presented his plan to Poroshenko and reckons the wall can be built in about six months.
Some analysts dismiss the idea as a stunt.
"In the short term, it cannot be done," said Volodymyr Fesenko of the Penta think tank. Another analyst, Mykhailo Pohrebinsky, said: "This is a public relations campaign meant to consolidate Kolomoisky's image as a Ukrainian patriot."
Despite such criticism, the proposal is not being dismissed in parliament as a crackpot idea.
"Whether or not it is Kolomoisky's project, a wall will be built to defend Ukraine from Russia's aggression," said Ivan Stojko, a parliamentary deputy from the Batkyvshina party led by former prime minister Yulia Tymoshenko.
Pavlo Rizanenko, a deputy from the Udar (Punch) party of former boxing champion Vitaly Klitschko, said: "I don't think Poroshenko has a monopoly on this idea. It's something that should have been done long ago."
The sight of rebels driving tanks in east Ukraine last Thursday increased the urgency of securing control of the border. Two days later, the rebels shot down a military plane with a missile, killing 49 servicemen.
Russia says it is not providing military support for the rebellion across much of the Donbass mining region. But its denials were undermined by satellite pictures released by NATO showing what it said were Russian tanks at a staging area close to the border days before similar tanks appeared in Ukraine.
The United States has also accused Moscow of supplying the rebels with T-64 tanks, MB-21 "Grad" multiple rocket launchers and other military vehicles.
Poroshenko, who replaced a Moscow-leaning president toppled in February after street protests, has ordered the armed forces to secure the frontier and says a 250-km (160-mile) stretch of the border has already been taken back. Once the border is secure, a truce can start and peace talks begin, he said.
His comments signalled a continuation of his dual policy of talking peace while pressing a military campaign in the east.
He wants Ukraine to demarcate the border on its own side, and build unspecified infrastructure there, which could mean erecting fences in villages that straddle the border.
Andriy Parubiy, the secretary of Ukraine's Security Council, estimated Russia had 16,000 soldiers on or near the border with Ukraine and 22,000 in Crimea, plus 3,500 in Moldova's breakaway Transdniestria region to the west.
Russia has balked at Kiev's proposals for tightening border security and says its moves are meant to fuel tension. But for some Ukrainians, building a wall has a clear appeal.
"Either we build a wall and forget about Russia, or let these madmen in Donbass live under (Russian President Vladimir) Putin. I'd prefer the wall and would be ready to give them some money to help build it," said Irina Sorokun, a Kiev pensioner.
$1 = 0.7345 Euros Additional reporting by Natalia Zinets and Pavel Polityuk in Kev, and by Alissa de Carbonnel in Moscow; Editing by Giles Elgood