A phone call between jailed WNBA star Brittney Griner and her wife Cherelle is being rescheduled after a failed attempt to connect on their anniversary, due to an "unfortunate" mistake.

The couple had not spoken since Griner's drug-related arrest in February, but attempts to connect through the United States Embassy in Russia were hindered since the phone line at the embassy was not staffed.

On Monday, it was discovered Griner tried to call 11 times over a period of several hours, dialling a number she had been given to patch the call through to her wife in Phoenix, but each call was left unanswered due to the unstaffed desk on Saturday.

US State Department spokesman Ned Price apologised for the "logistical error", confirming a rescheduled call will take place.

"We deeply regret that Brittney Griner was unable to speak with her wife over the weekend because of a logistical error," he told reporters.

"It was a mistake, it is a mistake that we have worked to rectify. As we said before, the call has been rescheduled and will take place in relatively short order.

"It was a logistical issue that was compounded by the fact that our embassy in Moscow is under significant restrictions in terms of its staffing, and so when we have issues with the telephone system there, for example, the technicians are not located on site. In fact, they're not even located in Russia."

Griner, the two-time Olympic gold medallist who plays for Phoenix Mercury and UMMC Ekaterinburg, was detained at a Russian airport in February after authorities there said a search of her bag revealed vape cartridges containing cannabis oil.

The US State Department designated her as wrongfully detained in May, while last week, Russian state news agency TASS reported a pre-trial detention had been extended until July.

For Cherelle Griner, the unanswered calls have had a demoralising effect.

"I find it unacceptable, and I have zero trust in our government right now," she told the Associated Press. "If I can't trust you to catch a Saturday call outside of business hours, how can I trust you to actually be negotiating on my wife's behalf to come home? Because that's a much bigger ask than to catch a Saturday call.

"This was such a big moment because this would have been the first time where I truly could tell if she's OK. This would have been the first time for me to actually just hear her in real time and to truly know if she's OK or to know if she's seconds away from not being in existence anymore."