By Crispian Balmer

ROME (Reuters) - "Italy should be proud of having a leader like him," Russian President Vladimir Putin said as he sat alongside Prime Minister Matteo Renzi last week. Mayoral elections on Sunday suggested Italians think otherwise.

Renzi's opposition to the European Union automatically renewing sanctions on Russia went down well when he visited St. Petersburg on Friday.

But back home, voters more worried about corruption and unemployment swept his Democratic Party (PD) from power in Rome and the northern industrial city of Turin two days later, handing control to the anti-establishment 5-Star Movement.

While the party held onto the financial capital Milan, it was toppled in a dozen major towns and cities in a result that augured ill for a referendum in October that Renzi has pinned his career on, promising to resign if he loses.

The referendum concerns constitutional reform, which Renzi says will bring political stability to Italy. Opposition parties see it as a vote on the prime minister himself, sensing a chance to oust him two years before his term expires.

"This is the end for Renzi," Renato Brunetta, parliamentary head of the center-right Forza Italia party, told Reuters.

When Renzi took office in 2014, he was a youthful, new force nicknamed "Demolition Man", promising to revitalize a country mired in recession, bureaucracy and corruption.

Now his assertive personality appears more of a hindrance than a help, with many voters yet to feel the benefits of his reform program and discontent rising within his divided party.

"We need to make clear that imposing things from on high does not bring the desired results," said Virginio Merola, a PD politician who held on as mayor of the northern city of Bologna in a rare success for the party.

"A do-it-yourself party does not work," he told reporters, taking aim at Renzi's management style, which critics say is overbearing, arrogant and self-centered.

BIG BUSINESS

Renzi did not take part in campaigning for Sunday's second-round run-off vote, a sign that PD candidates did not regard him as an asset. He preferred to go instead to Russia to drum up contracts for Italian companies.

Business leaders have praised his can-do style of government and his efforts to help boost trade. "He is very different from past prime ministers. They used to call up asking for favors. He calls up asking what he can do to help," said a senior executive in energy company Eni, who declined to be named.

His ties with big business have angered some stalwarts of the PD, the center-left successor of Italy's defunct Communist Party. Traditionalists say he should spend more energy on tackling the problems of the party's working class electoral base.

Although the economy is now growing after the worst downturn since World War Two, it still lags EU peers, and unemployment remains stuck above 11 percent despite a shake up of the labor market which Renzi touts as his main economic achievement.

"Talking to industrialists and the middle class has not brought Renzi the votes he had hoped for," said Piero Ignazi, a professor of comparative politics at Bologna University.

"He has made strategic errors, but he is also the best Italian politician of the last 30 years and is perfectly capable of changing his spots overnight," Ignazi told Reuters.

After disappointing results in the first round on June 5, Renzi pinned the blame on party divisions, threatening to take a "flamethrower" to the PD to impose his authority.

Since he seized control of the party in 2013, he has faced resistance from influential veterans such as former prime minister Massimo D'Alema.

"I would vote for the devil if that meant I could get rid of Renzi," D'Alema was quoted as saying by la Repubblica newspaper last week. He denied making the comment, but also refused to back publicly the PD's beleaguered candidate in Rome.

"There is a plot to oust Renzi which is being played out in broad daylight," said life-long PD voter Francesco Poggi, a retired bus driver who attended a low-key rally on Friday to wrap up the PD's disastrous mayoral campaign in Rome.

"The party has been too gentle with these people," he said, referring to the party's old guard. "It needs to put its house in order."

BACKROOM DEALS

Such a crackdown now could prove fatal, with Renzi needing to keep the peace before the October referendum, analysts said.

An opinion poll on Sunday put backing for the proposed constitutional reform - which would abolish the Senate as an elected chamber and sharply restrict its ability to veto legislation - at 28.6 percent. Opposition was at 27.2 percent and undecideds on 44.2 percent.

Should he win, Renzi would have carte blanche to reshape the party and eliminate dissidents but even then his problems would be far from over.

Sunday's election showed that Renzi is vulnerable to the anti-establishment sentiment that has emerged across Europe in since the debt crisis.

The PD held its own against traditional center-right rivals, including in Milan. But the 5-Star Movement won 19 of the 20 battles it took part in, appealing to voters of all political colors with its promises to beat back corruption and renounce old-style backroom deals that have defined politics.

Under a new electoral law that will be used in the next national vote, it looks highly likely that the PD and 5-Star Movement will face each other in a national run-off. Sunday's results suggest Renzi would lose.

"A new breed of 5-Star leaders has popped up from nowhere, and for now, Renzi doesn't seem to have an answer to them," said politics professor Ignazi.

(editing by David Stamp)