Griner was speaking at the second hearing of her trial on the narcotics charge that could see her sentenced to up to 10 years in prison, days after she urged U.S. President Joe Biden to secure her release.
"I'd like to plead guilty, your honour. But there was no intent. I didn't want to break the law," Griner said, speaking quietly in English which was then translated into Russian for the court.
"I'd like to give my testimony later. I need time to prepare," she added.
The next court hearing was scheduled for July 14.
Griner's lawyer Alexander Boykov told reporters they were hoping for the most lenient sentencing possible.
The two-time Olympic gold medallist was detained in February at Moscow's Sheremetyevo airport with vape cartridges containing hashish oil, which is illegal in Russia, and has been kept in custody since.
In a handwritten note, she appealed to Biden directly earlier this week to step up U.S. efforts to bring her home.
"I realize you are dealing with so much, but please don't forget about me and the other American detainees..." Griner wrote. "Please do all you can to bring us home."
Biden spoke to Griner's wife on Wednesday, telling her he was working to have her released "as soon as possible", the White House said.
U.S. officials and many athletes have called for the release of Griner - or "BG" as she is known to basketball fans - who they say has been wrongfully detained.
Her case has also prompted concerns that Moscow could use it as leverage to negotiate the release of a high-profile Russian citizen in U.S. custody.
Russian authorities say there is no basis to consider Griner's detention illegal and that the case against her is not political despite Moscow's fraught relations with United States over the Russian military intervention in Ukraine.
Moscow's Deputy Foreign Minister Sergei Ryabkov said on Thursday that it was difficult to exchange prisoners with the United States and suggested Washington stop talking about the fate of Griner.
Griner, a centre for the Phoenix Mercury in the Women's National Basketball Association, had played for UMMC Ekaterinburg in the Russian Women's Basketball Premier League to boost her income during the WNBA off-season, like several other U.S. players.
The Russian foreign ministry has said Griner could appeal her sentence or apply for clemency once a verdict has been delivered.
(Reporting by Reuters; editing by Guy Faulconbridge, Mark Trevelyan, Angus MacSwan and Jonathan Oatis)
