KIEV, Oct. 6 - Since a new government swept into power two years ago, Ukraine’s central bank has won accolades for a major overhaul of the country’s financial sector—with a big caveat, The Wall Street Journal reported.

The National Bank has shut down 82 ailing banks and brought clearer accounting and better disclosure of bank ownership. But it has stalled out at Privatbank, the country’s largest private financial institution.

The lender is controlled by Ihor Kolomoisky, who bankrolled armed formations supporting the Ukrainian military in its fight against Russia-backed separatists in the country’s east. It holds a third of the country’s total deposits and handles about 75% of all payment transactions.

While Privatbank says it earned the equivalent of $10.7 million in 2015, it is also sitting on a pile of loans to related companies that analysts believe accounts for at least 40% of its total loan book.

The National Bank has pushed other banks in Ukraine to reduce related-party lending and recapitalize, taking away the licenses of those that don’t comply. But the central bank has been reluctant to tackle Privatbank, which investors and analysts say could threaten the credibility of the cleanup effort.

“There is still one very big question mark, and that is Privat,” said Gerhard Boesh, first deputy chairman of Raiffeisen Bank Aval, Ukraine’s fifth-largest bank.

National Bank officials have described Privatbank as the only private institution among the country’s three strategically important banks. That makes it key to Ukraine’s fragile economy, which is expected to grow by just 1% this year after deep contractions in 2014 and 2015.

Moody’s Investors Service ranks the bank one level above its default rating, saying about a third of its loans are individually impaired and that “asset quality of the bank will likely remain under pressure.”

“If Privat goes bust, the country goes bust,” said Pavlo Rizanenko, a legislator from the pro-presidential faction of parliament.

Kolomoisky didn’t respond to requests for comment. Privatbank Chief ExecutiveOleksandr Dubilet said in an interview that shareholders injected the equivalent of about $78 million in new capital into the bank this year, after pumping in about four times that amount last year.

“We have done everything we have to do,” said Mr. Dubilet. “I think if the bank will need further capital, the shareholder will manage.”

For years, Ukraine’s banks functioned largely as personal financing arms for the country’s richest men.

"They had to have a football club, a newspaper, a lover, and the bank for your lover,” former National Bank Deputy Gov. Vladislav Rashkovan joked in an interview this summer before leaving the central bank in August.

The result has been a crippled banking sector in which 53% of the loans at the top 20 banks aren’t performing, according to the National Bank.

The National Bank has pushed for laws requiring deeper disclosures of bank ownership, which was often hidden by complicated structures that some officials dubbed “football teams.” The central bank also has been conducting stress tests and demanding better, more transparent accounting.

The country’s second-largest private lender, Delta Bank, was shut down after its main shareholder failed to keep up with a capital-injection plan last year despite repeated warnings from the central bank.

Many argue that Privatbank’s size and Kolomoisky’s stature have allowed the bank to continue playing by different rules. The businessman is an important player in Ukraine’s politics, owning one of the country’s most popular television channels, and his open backing of a group of lawmakers can help influence votes. Kolomoisky’s businesses also control a 42% stake in the country’s state oil-extraction company, Ukrnafta.

In interviews with Ukrainian outlets, Kolomoisky has said Privatbank functions as a normal bank and that he doesn’t intend to use it to gain political leverage.

Privatbank says related-party lending accounts for 17.7% of its loans. Anastasia Tuyukova, an analyst at Dragon Capital, Ukraine’s largest investment bank, puts it higher, at 40% to 80% of the total, based on the industries represented in Privatbank’s loan book.

Uncertainties about Privatbank’s asset quality and loan book make it unclear how much additional capital it might need. Tuyukova estimated the bank could need anywhere from $1 billion to $4 billion, far beyond what Privatbank’s shareholders have pledged so far. (wsj/ez)