The presidency of Interpol is in many ways a ceremonial position with little power to influence the issuance of warrants. Nevertheless, elevating a Russian in the face of such criticism would be a public relations coup for Mr. Putin. It would also be a setback for international lawyers, who have credited Interpol as taking steps in recent years to tighten administrative controls.

“If you have an organization where part of the job is to keep the chickens safe, and the head of the organization — O.K., he doesn’t really do much, but he’s a fox? It sends a message,” said Michelle Estlund, an American defense lawyer who tracks Interpol and its issuance of red notices. “They can say, ‘Don’t worry, the fox doesn’t really guard the hen house.’ But he’s there.”

The president is selected by the Interpol General Assembly, which is made up of delegates from its member countries. Each country gets one vote, there is no veto, and the winner must carry two-thirds of the vote. Former colleagues say Mr. Prokopchuk, a current vice president, is regarded as well qualified, and members are encouraged to vote for the individual, not the country.

Image Aleksandr V. Prokopchuk is the Russian candidate for president of Interpol. Credit... Valery Sharifulin/TASS, via Getty Images

Mr. Prokopchuk, a university graduate who speaks six languages, does not fit the image that many foreigners — and many Russians — have of Russian police officers as boorish brutes. He is well spoken, highly educated and has a long record of pushing for closer cooperation between police services in Russia and the West.

American and European diplomats are backing Mr. Prokopchuk’s chief opponent, Kim Jong-yang of South Korea. American officials said they would not discuss their efforts, saying the vote would be carried out in secret.

But the deputy attorney general, Rod J. Rosenstein, addressed the Interpol conference this week and took aim at governments that provided safe havens to cybercriminals while trying to game the international warrant system — criticisms that the United States has had of Russia for years.