Cambridge Analytica has been a political flash point since its role in the Trump campaign attracted scrutiny after the election. While Mr. Nix’s firm turned over some records to the House Permanent Select Committee on Intelligence during its investigation of Russian interference, Democrats on the committee want a fuller review. “It is imperative to interview a broader range of individuals employed by or linked to Cambridge Analytica,” they said in a report this month.

Asked about the Russian oil company, a spokesman for SCL said that in 2014 the firm’s commercial division “discussed helping Lukoil Turkey better engage with its loyalty-card customers at gas stations.” The spokesman said SCL was not ultimately hired.

Arash Repac, chief executive of Lukoil Eurasia Petrol, offered a different explanation for the talks. He said that a meeting he attended with SCL in Turkey involved a promotional campaign with local soccer teams.

“We needed somebody to guide us with the customer data that we were collecting,” he wrote in response to a question from The Times. “Even though our campaign went ahead, we decided not to cooperate with SCL. No contracts were signed.”

But Christopher Wylie, who helped found Cambridge Analytica and develop the company’s voter-profiling technology, said Lukoil showed interest in how the company used data to tailor messaging to American voters.

“I remember being super confused,” said Mr. Wylie, who took part in one of the Lukoil meetings.

“I kept asking Alexander, ‘Can you explain to me what they want?’” he said, referring to Mr. Nix. “I don’t understand why Lukoil wants to know about political targeting in America.”