MOSCOW — The Russian elite, the group of oligarchs and other loyalists around President Vladimir V. Putin who amassed great wealth over nearly two decades of hand-in-glove work with the government, is showing signs of cracking.

As the economy stagnates amid international sanctions and low oil prices, a high-profile bribery case has illustrated how the country’s most privileged players have taken to fighting over slices of a smaller economic pie, seeking an advantage over rivals through the courts and law enforcement officials who are widely seen as vulnerable to corruption.

In recordings read aloud by prosecutors in a case being heard in a Moscow courtroom, two men, both Kremlin insiders, are first heard in an assiduously polite conversation recorded by secret listening devices, even as one was preparing to doom the other to a long spell in prison.

With a warmth betraying nothing of what was to come, Igor I. Sechin, the powerful director of Rosneft, Russia’s national oil company, invited Aleksei V. Ulyukayev, then the economy minister, to a meeting and even called him “dear.”