Sibur’s top ownership — including Gennady Timchenko, who is Mr. Putin’s friend and judo partner and is subject to American sanctions, and Kirill Shamalov, who is married to the Russian president’s youngest daughter — makes it “a company with crony connections” in Moscow, said Daniel Fried, a Russia expert who served in senior State Department posts in Republican and Democratic administrations.

Another of Navigator’s major customers is PDVSA, the Venezuelan state oil company, controlled by the authoritarian regime of Nicolás Maduro. The Trump administration imposed sanctions on PDVSA this summer.

In a written response to questions by the Times, James Rockas, a spokesman for Mr. Ross, said that Navigator’s relationship with Sibur began before Mr. Ross joined the board in March 2012, and that he had never met the Russian oligarchs who are Sibur’s major shareholders. Public records show that Mr. Ross’s firm became a major investor in Navigator in November 2011, three months before the company chartered its first ships to Sibur.

“Sibur was not under sanctions at the time the contract was signed and is still not subject to sanctions,” Mr. Rockas said.

More broadly, he said that Mr. Ross “recuses himself from any matters focused on transoceanic shipping vessels, but has been generally supportive of the administration’s sanctions of Russian and Venezuelan entities.”

“Secretary Ross has never had to seek, nor received, any ethics exemption,” Mr. Rockas said, “and he works closely with Commerce Department ethics officials to ensure the highest ethical standards.”

It is perhaps unsurprising that Navigator would have a relationship with a major Russian company during Mr. Ross’s tenure. Much like President Trump, whose company sought approval for a hotel project in Moscow as recently as last year, Mr. Ross has long shown an appreciation for the untapped potential of Russian markets when seeking investment opportunities. His involvement there dates at least to the 1990s, when he was appointed by President Bill Clinton to the board of the U.S. Russia Investment Fund, established to promote American business interests in Russia.