Escorted by a masked police officer with a dog, with her wrists handcuffed, the American basketball star Brittney Griner appeared in a Russian court on Tuesday for another hearing in a trial that is likely to end with her conviction in the middle of this month, her lawyers said.

One of the best players of her generation, Ms. Griner has been caught in a high-stakes rivalry between Moscow and Washington that has turned into outright confrontation with Russia’s invasion of Ukraine. And as the case is heard in a courtroom, the wrangling over Ms. Griner’s fate has shifted increasingly to the diplomatic arena, with Russia and the United States signaling her possible involvement in an exchange for high-profile Russians held in custody in the United States.

Last week, Secretary of State Antony J. Blinken said the American government had “put a substantial proposal on the table,” although he declined to discuss the details. On Thursday, he discussed the matter with his Russian counterpart, Sergey V. Lavrov, in their first phone call since the war in Ukraine. But no breakthroughs were reported, and no progress is expected before a judge in the town of Khimki near Moscow delivers a verdict in the case.