Critics condemned Uber over its screening practices when it emerged that the driver had previously been detained for months on suspicion of rape in a different case. Uber responded to the episode by introducing increased safety measures in its vehicles, including a kind of panic button for passengers who felt unsafe. Uber eventually settled a lawsuit the woman filed against the company; the driver was convicted of rape.

The attack came at a fraught time for Uber. The company was banned in Delhi after the story broke, putting at risk Uber’s plan to dominate the market in India, a country of more than 1.3 billion people that the company hoped would fuel enormous growth. Uber had also just closed a $1.4 billion round of financing, and was in the middle of talking to other companies about more financing.

Mr. Alexander was convinced that the rape charges were part of a plan hatched by Ola, the leading ride-hailing company in India and one of Uber’s largest Asian competitors, according to two of the people familiar with the matter. He spent months in India as Uber established itself there, and conducted his own investigation. He shared his concerns with Mr. Kalanick and Mr. Michael, who were also fixated on the case, according to the two people.

Mr. Kalanick and Mr. Alexander had long telephone conversations about what they believed to be subterfuge on the woman’s part, trying to figure out how to rectify the situation, according to two people familiar with those talks. Mr. Alexander carried the woman’s records, which he believed were at odds with her account, with him. The ban imposed on the company in Delhi added to their suspicions.

Uber declined to comment on the firing of Mr. Alexander, and he did not respond to a request for comment. Recode first reported news of his termination.

Current and former Uber employees were surprised to learn that Mr. Alexander was not one of the 20 employees that Uber said on Tuesday it had fired. He was let go only after reporters asked Uber about his actions, despite several high-level executives having knowledge of the matter, according to two of the people familiar with the matter.

For now, Uber employees are awaiting the results of Mr. Holder’s investigation. The company is expected to address his findings at a meeting for all employees on Tuesday.