MOSCOW — When a new government-backed investment fund opened five years ago, Moscow wanted to send a simple message: Russia was ready to take the politics out of business.

Authorities signed up a high-powered board of international advisers to oversee its activities, a group that included American private equity executives like David Bonderman of TPG and Stephen A. Schwarzman of the Blackstone Group. In a video on the fund’s site, Mr. Bonderman emphasized that the investments in Russia would be “transparent and make commercial decisions, not political decisions.”

After the United States and Europe slapped Russia with sanctions over the Ukraine conflict, many board members distanced themselves. And recently, the fund has faced an uncomfortable spotlight over a big investment to a politically connected company. Late last year, the Russian Direct Investment Fund made a $1.75 billion loan to Sibur, a giant petrochemical company with close ties to the Kremlin.

Such concerns have long clouded the investment landscape, that politics play a heavy hand in business. And they have only intensified with the current economic malaise, as the government struggles to deal with weak oil prices and Western sanctions.

One of Sibur’s major shareholders, Gennady N. Timchenko, has decades-long ties to President Vladimir V. Putin of Russia. Mr. Timchenko is under United States sanctions as a member of the “inner circle.”

Another big owner, Kirill N. Shamalov, is the son of Nikolai T. Shamalov who has similarly received sanctions for his connection to Mr. Putin. Kirill Shamalov is also widely reported in Russian and Western news media to be the son-in-law of Mr. Putin.

“When the economic crisis deepens, and this floats to the surface, it could be a serious blow to Putin,” Stanislav A. Belkovsky, a political analyst, said of lending to a figure linked to Mr. Putin’s family.

The Russian Direct Investment Fund defends the Sibur deal, saying it follows the fund’s investment guidelines. The chief executive, Kirill Dmitriev, in a written statement, characterized the loan as commercially motivated and issued “in line with our established practices.”

Mr. Putin, like many Russian officials, refuses to discuss his family or reveal family business activities. Mr. Shamalov has declined to confirm or deny whether he is married to the younger of Mr. Putin’s two daughters; a representative for Mr. Shamalov did not respond to written questions. Sibur said in a statement that the company would not comment on “speculation” that a shareholder is a son-in-law of the president and said that shareholders in any case had no role in negotiating financing.

Mr. Shamalov’s company, Ladoga Management, declined in a statement to say whether he is a son-in-law of Mr. Putin, asserting that, “like every other person, Kirill Shamalov has the right to privacy.”

“The Soviet tradition was the relatives should not be in the public eye,” said Mr. Belkovsky, the political analyst.

Former President Dmitri A. Medvedev established the fund in 2011 with the explicit goal of restoring confidence in Russia’s investment climate.

Mr. Medvedev wanted to attract overseas investors to the country’s companies, and tried to entice them by matching state funds with private capital. The partnership with the state, the theory went, would reduce the investors’ worries about the risk of nationalization and arbitrary regulation.

To further shore up support, the fund rounded up prominent investors to serve on the advisory board. Along with the TPG and Blackstone executives, the fund recruited Leon Black of Apollo Global Management; Richard M. Daley, the former mayor of Chicago; Kurt Björklund of Permira; and Chinese and Middle Eastern fund managers.

By lending their names to the fund’s advisory board, these financial heavyweights were supposed to ensure that money did not flow to political pet projects. The first wave of deals focused on bread-and-butter investments in companies building out Russia’s infrastructure and catering to the middle class.

In a typical investment, the fund and the American investment management company BlackRock in 2012 together poured $50 million into a chain of private hospitals called Mother & Child. With more Russians watching movies, the fund also invested $100 million into a multiplex business, along with Baring Vostok Capital Partners, a Russian private equity company.

But western players backed away after the sanctions targeted the fund’s parent bank, Vnesheconombank, a major Russian state-owned bank, in response to Russia’s intervention in the eastern Ukraine war. Mr. Schwarzman and Mr. Bonderman withdrew their names from the published list of advisers in 2014.

Blackstone and TPG declined to comment about the Russian fund.

With Russia’s economy slowing and funding drying up, the government allowed the Russian Direct Investment Fund to tap into the resources of the National Welfare Fund, a sovereign wealth fund that is part of the country’s pension system.

In two deals, the Russian Direct Investment Fund helped invest about $800 million of this pension system money into companies building electrical power lines and expanding broadband Internet access to rural areas.

An even bigger investment with Sibur soon followed.

In December, the fund disclosed an investment totaling $5.05 billion for Sibur to build a petrochemical factory in the Siberian city of Tobolsk, to make precursor chemicals for plastics and synthetic rubber.

The Russian Direct Investment Fund and foreign investors, including unspecified Middle Eastern sources and two German funds that tie financing to the export of German industrial goods, raised $3.3 billion. Such moves fulfilled the fund’s mandate to raise private sector capital.

The Russian Direct Investment Fund also arranged the $1.75 billion loan from the National Welfare Fund. It was structured as below-market-rate bonds sold to the sovereign wealth fund.

“You can see the conflict of interest here,” Vladimir A. Ryzhkov, a former deputy speaker of the Russian Parliament, said in a telephone interview. The National Welfare Fund, he said, is legally obliged to cover pension system deficits like those existing in Russia today because of the oil price slump. Pensions this year will decline relative to inflation.

“The president controls the resources in these funds,” Mr. Ryzhkov said, “and if his son-in-law is a part owner of this company, there is a conflict.”

Sibur is one of Russia’s largest petrochemical companies, processing the country’s rich supplies of oil and natural gas into plastic, synthetic rubber and other goods. From an industrial policy perspective, the company’s activities help diversify Russia’s economy by creating value-added products from its resources.

In a statement announcing the funding, Mr. Dmitriev, the Harvard-trained chief executive of the Russian Direct Investment Fund, a former Goldman Sachs banker and McKinsey & Company consultant, praised the loan to Sibur as “a milestone in Russian industry and infrastructure development.”

But the connection to Mr. Putin has attracted attention, in part because of the veil of secrecy that surrounds his family.

At a news conference on Dec. 17, Mr. Putin faced questions about his two grown daughters. As usual, he declined to disclose details about his family. He denied that his daughters were involved in business, and offered few clues about their activities.

A journalist from RBC, a Russian newspaper that has investigated Mr. Shamalov’s business dealings, asked Mr. Putin whether his daughter, born Yekaterina Putina, has been living in Russia under the assumed name of Katerina Tikhonova.

Earlier, RBC reported on a sprawling development project on land partly owned by Moscow State University run by a woman named Katerina Tikhonova, 29, who had been seen in public with Mr. Shamalov. Later, a Russian blogger, Oleg Kashin, identified Ms. Tikhonova as Mr. Putin’s daughter in a post called “It’s Her.” Reuters and Bloomberg both detailed the couple’s wedding.

Mr. Putin declined to answer questions about his family at the conference.

“I read, of course, on the Internet and in some other publications about Yekaterina Tikhonova, just as I’ve read things about other possible relatives and daughters at different times,” Mr. Putin said, according to a Kremlin transcript. He said his daughter is living in Russia, but declined to say whether she is Ms. Tikhonova.

“I am proud of them,” he said, speaking of his two daughters.

“They are taking just first steps in their careers, but already achieved successes,” he added. “They are not in business or politics, and are not sticking their nose into anything.”