The two-time Olympic gold medalist, who stars for the Phoenix Mercury but who plays for a Russian basketball team during the WNBA off-season, was arrested in February.
Russian authorities said she had cannabis oil in her luggage and accused her of smuggling significant amounts of a narcotic substance — an offense punishable by up to 10 years in prison.
The US State Department has since classified Griner as wrongfully detained in Russia and her case is being handled by the office of the US Special Presidential Envoy for Hostage Affairs (SPEHA) Roger Carstens.
“The league — and by that, both the WNBA and its brother league, the NBA — we have a huge responsibility to Brittney. Griner’s one of our players,” Silver told ESPN.
“Part of our decision to not to take a higher profile here, frankly, came at the suggestion of experts in and out of government who felt the best path to getting Brittney out was not to amplify the issue.
“Having said that, there’s an enormous role for the public to play through protests or letting their representatives know how strongly they feel about this. So we’re working.
“Cathy Engelbert, the commissioner of the WNBA, is on this issue every single day. I’m working side-by-side with her. We’ve been in touch with the White House, the State Department, hostage negotiators, at every level of government and also through the private sector as well.
“Our number one priority is her health and safety and making sure that she gets out of Russia.”
WNBA season starts
It comes as Secretary of State Antony Blinken spoke to Griner’s wife on Saturday as her imprisonment in Russia continues.
According to a senior State Department official, the top US diplomat told Cherelle Griner that her wife’s release is a top priority for the department and has his full attention.
Blinken said the State Department is working on the case day and night, and that Cherelle should not to hesitate to reach out if there’s anything she is not getting.
On Friday, a Russian court extended Brittney Griner’s pretrial detention until at least June 18.
Griner was the No. 1 pick in the 2013 WNBA draft and is one of the league’s all-time best players.
The league, which started its 26th regular season without Griner, is honoring the seven-time all-star with her initials and jersey number (42) along the sidelines of all 12 home courts. Griner will also be paid her full WNBA salary, the league said.
Last season, Griner finished second in Most Valuable Player award voting. The 6-foot-9 center led the Mercury to the WNBA Finals, where Phoenix lost to the Chicago Sky.
CNN’s Jennifer Hansler, Ellie Kaufman, Homero DeLaFuente, Wayne Sterling, Aya Elamroussi and Steve Almasy contributed to this report.