Griner’s supporters are imploring the Biden administration to secure her release.

Brittney Griner’s family and supporters are increasingly imploring President Biden and the U.S. government to secure her release amid continuing fears that she could be used by Russia in the geopolitical jousting over its war in Ukraine.

Her agent, Lindsay Kagawa Colas, recently coordinated a letter to Mr. Biden and Vice President Kamala Harris signed by groups including the National Organization for Women, the Human Rights Campaign, the National Urban League and the National Action Network. The letter called for the government to strike a deal for her release.

U.S. State Department officials met in June with Ms. Griner’s W.N.B.A. team, the Phoenix Mercury, to discuss the status of her monthslong detention in Russia and efforts made toward securing her release.

Ms. Griner’s supporters have been vocal their support for her release. Many W.N.B.A. players have worn T-shirts and hoodies in support of her, and her initials are displayed on the courts for all 12 W.N.B.A. teams.

Initially, Ms. Griner’s supporters spoke little publicly about the detention, fearing her situation would become part of the larger global conflict involving Russia’s invasion of Ukraine and the United States’ strained relationship with Russia.

That strategy shifted after the State Department declared Ms. Griner had been “wrongfully detained” days after Russia exchanged Trevor R. Reed, a former U.S. Marine who had been sentenced to nine years in prison for assault, in a prisoner swap.

Mr. Reed’s deteriorating health in Russia most likely played a factor in Moscow’s willingness to release him, said Kimberly St. Julian-Varnon, a Ph.D. student in the history department at the University of Pennsylvania, whose areas of study include African American experiences in the Soviet Union, Ukraine and Russia.

Ms. St. Julian-Varnon, who has consulted with the W.N.B.A. players’ union about Griner’s detainment, said: “The problem is Brittney, politically, is worth so much more in terms of the trading of prisoners than Trevor Reed because of her profile. So the ask is going to be much bigger, and I think the ask that they’ve been telegraphing in the Russian news is for Viktor Bout.”

Mr. Bout, an international arms dealer, was convicted by an American court and sentenced to 25 years in prison. Russia also has interest in freeing Roman Seleznev, a hacker who was convicted in the United States for running a massive credit card and identity theft operation and sentenced to 27 years in prison. Besides Ms. Griner, Russia has also detained Paul Whelan, a former U.S. Marine sentenced to 16 years on espionage charges.

“This is the classic dilemma of hostage situations,” said Thomas Firestone, a former Justice Department official who worked in Moscow as a lawyer. “If you negotiate for the release, you may be encouraging future hostage taking. If you don’t, the person may never be released.”

Jake Sullivan, Mr. Biden’s national security adviser, told reporters on Tuesday that he and Secretary of State Antony J. Blinken had spoken to Ms. Griner’s wife, Cherelle Griner, in recent days.

“The United States government is actively engaged in trying to resolve this case and get Brittney home,” Mr. Sullivan said. He added: “It has the fullest attention of the president and every senior member of his national security and diplomatic team. And we are actively working to find a resolution to this case and will continue to do so without rest until we get Brittney safely home.”