Georgia's billionaire prime minister Bidzina Ivanishvili looks surprised at the suggestion that he might be a touch sensitive to criticism.

"Quite the opposite," he insists, enunciating his words very carefully, in lightly accented Russian. "I really love criticism! Everyone who knows me knows that."

Anyone who has followed Georgian politics recently could be forgiven for believing the opposite to be true. And even the man himself admits that he wishes the populace and media would sometimes be a bit more generous with plaudits, especially given that he has "done everything right" during his year in politics.

"Society should not just criticise; it should also praise the government when it works well," says Ivanishvili, now in a gently hectoring tone. "That should be felt too, but it is missing from society at the moment."

Ivanishvili, who made a vast fortune in 1990s Russia and has been ranked by Forbes magazine as one of the 200 richest people in the world, lived as a recluse until he entered politics in 2011. In elections last October he surfed a wave of popular discontent directed at Mikheil Saakashvili, president of Georgia since the 2003 "rose revolution". He united a motley group of everyone from urbane intellectuals to frothing-at-the-mouth nationalists into the Georgian Dream coalition and won an overwhelming parliamentary majority.

One year on, Ivanishvili receives the Observer during a religious festival in the city of Mtskheta, the ancient former capital of Georgia. He wears an immaculate suit and his short greying hair is swept back.

Outside the window of our meeting room is an 11th-century cathedral, its courtyard filled with beggars, pious believers crossing themselves. Priests with black robes and luxuriant beards are moving among the flock. It is a reminder that, for all of Saakashvili's reforms, away from the bright lights and alfresco cafes of central Tbilisi, Georgia is still largely rural, conservative and crushingly poor.

Critics say his year in power has been disastrous politically, economically and diplomatically, in terms of relations with Russia. Ivanishvili, naturally, disagrees: "It's all just shouting and emotions… We are moving in the right direction."

But the widespread expectation that the billionaire's money would trickle down in the direction of ordinary Georgians has gone unfulfilled, and Ivanishvili finds himself coming to the end of his honeymoon with the electorate. With elections to the newly diminished presidential role coming up, Ivanishvili says that when they are completed he will nominate a new figure to replace himself as prime minister and retreat back into the shadows.

Saakashvili's team of young enthusiastic reformers made sweeping changes to Georgia, taking it from the brink of a failed state to an inchoate democracy. But then came the devastating 2008 five-day war with Russia, crackdowns on protests, and accusations of creeping authoritarianism, which in time became ever harder to ignore.

After the high-octane revolutionary leader, many had felt that the country needed a bit of a breather. In the later Saakashvili years it has been a common refrain among diplomats in Tbilisi that Georgia could do with "someone boring" to calm the waters.

But instead of the competent, understated technocrat that it perhaps needed, the country elected a character who seemed to have strolled out of a tale penned by an overimaginative novelist. A reclusive oligarch who lived in a contemporary chateau perched on the hillside above the capital city, Ivanishvili was the richest man in the country but no one even knew what he looked like.

There were all kinds of rumours about the Wizard of Oz figure hidden inside the weird glass castle: that he travelled the country incognito and doled out sacks of cash to artistic or social causes he deemed worthy; that he had a teenage albino son who secretly recorded rap tracks with leading US hip-hop stars; that he kept pet zebras, lemurs and kangaroos at his various palatial residences; and even that he imported fresh fish from Antarctica to ensure that his collection of penguins did not get depressed by Georgia's unsuitably warm climate.

He was the mystery figure who had financed many of Saakashvili's reforms, but the two men had a falling-out of epic proportions and were now sworn foes. As it later turned out, almost all the rumours were true.

After a year in charge, his project to turn Georgia into a perfect European democracy is "on track", he says, but has been assaulted by what he sees as obstructiveness from Saakashvili, who reaches the end of his second and final term as president when elections for the post are held next Sunday.

Ivanishvili has nominated a candidate, Giorgi Margvelashvili, with little frontline political experience. However, he is leading in the polls despite what the billionaire feels is an abundance of scurrilous gossip and unfounded criticism from the media.

Earlier this month Ivanishvili summoned several Georgian journalists for a four-hour dressing down, broadcast live on television, in which he read the journalists' quotes back at them from a sheaf of papers and demanded they account for their words. He berated them for reporting facts without checking them and thus becoming "postmen, not journalists". He held a similar meeting with political analysts.

Ivanishvili denies that such irritation at criticism is a result of living the mollycoddled life of the oligarch, surrounded by oily sycophants. The way he sees it, he simply wants people to get their facts straight.

"Those journalists and experts, I asked them: 'Look, you're saying this, this and this, but where are your arguments? You've got no arguments!' They couldn't prove anything and then they were all offended. 'Oh look, he doesn't like criticism,' they said! Please, criticise me, but you need to do it with arguments and not say things that are not true."

He is not keen on the foreign press coverage of his time in office either. His PR aides complain that foreign journalists persist in writing about the prime minister's zebras, instead of his policies, probably because Ivanishvili keeps insisting on meeting journalists at his zebra-filled summer retreat rather than, say, in an office. Show a journalist a pet zebra, and the journalist will probably write about the zebra first and planned agricultural reform second. This is something that, after a year of showing zebras to journalists, Ivanishvili has apparently still failed to grasp.

Several members of his team say they genuinely believe that the prime minister wants the best for Georgia, and even opposition figures no longer seriously entertain their earlier claims that he is a Kremlin stooge, but many privately admit that he is not the best at taking advice from others, or at getting his message across to the media.

In an opaque scheme that no one but he understands entirely, Ivanishvili plans to appoint a new prime minister shortly after the presidential elections and retreat from politics, becoming a kind of omnipresent benefactor, providing cash and "control" to the government.

It sounds a bit ominous. Does he accept that, as a clearly partisan political figure, it will be hard for him to accept the role of a neutral benefactor of civil society?

"But I won't be a politician any more," he says, matter of factly, as if by stepping away from the fiercely political battle of which he has been one half, he can suddenly acquire neutrality.

Shortly after meeting the Observer, he went on Georgian television to tell voters that unless at least 60% of them back his preferred presidential candidate, he will be offended and "lose enthusiasm" for his initiatives, essentially blackmailing Georgians with turning off the cash taps if they do not vote as he says.

Giga Bokeria, a key member of Saakashvili's team, sees Ivanishvili's decision to leave politics through the prism of his oligarchic background. According to Bokeria, the billionaire has deliberately picked a weak and politically inexperienced figure as candidate for president and is likely to pick another novice politician to succeed him as prime minister.

"The dream of all oligarchs in 1990s Russia was to control politics from behind the scenes," he says. "Of course, in Russia, they chose the wrong figure in Putin, and it all went wrong."

Ivanishvili is not particularly reassuring about how his behind-the-scenes role really will facilitate the growth of the "perfect European democracy" he says he is building.

"Together with society, I will control the government which I leave behind," he says. "I would prefer not to reveal the mechanism for now, the way in which I will act."