Interpol’s tepid response to that highly unusual action sparked criticism that it was too quick to yield to influence from an authoritarian government. Mr. Stock did not directly address those criticisms but said, “Interpol has to work in a space neutral to geopolitics, but not of course neutral to human rights.”

Mr. Kim has served as interim president of Interpol since Mr. Meng’s disappearance. Mr. Prokopchuk has served as a vice president of the organization and is well regarded by his colleagues.

But Mr. Prokopchuk has also worked for more than a decade in a Russian department that has flooded Interpol with requests for international warrants, known as red notices, seeking the arrest of political dissidents and others. Interpol has rejected requests that it viewed as baldly political, but the Russian government has at times found workarounds by seeking a different type of warrant, known as a diffusion. Diffusions are circulated through Interpol but do not get reviewed there.

The investor Bill Browder, one of the highest-profile Kremlin critics, is the most public target of this effort. The Russian government has repeatedly sought his arrest. Early this year, he live-tweeted his detention in Spain on a warrant issued out of Moscow.

On Tuesday, Mr. Browder held a news conference in London and warned that President Vladimir V. Putin of Russia was trying to use Interpol to intimidate his opponents.

“This is a perfect way for Putin to basically breathe the fear of God into all of his enemies,” he said. “So they know they can’t even escape Russia if one of his guys is at the head of Interpol.”

The presidency is in many ways a ceremonial position at Interpol, where executive power is held by the secretary general. Former Interpol officials said that if he had become president, Mr. Prokopchuk would have had little ability to influence the issuance of red notices. They said that Interpol delegates are encouraged to vote on the merits of individual candidates, not on their home countries.