The WNBA star, who also played in Russia, could face 10 years in prison if convicted.
Griner's trial which began on July 1 resumed Thursday .
"I'd like to plead guilty, your honor. But there was no intent. I didn't want to break the law," said Griner, speaking English, which was then translated into Russian for the court.
Griner told the court she needed "time to prepare" her testimony.
On Monday, Griner sent a letter to U.S. President Joe Biden pleading he provide assistance to her and other Americans detained or held hostage in Russia.
White House press secretary Karine Jean-Pierre said Tuesday that Biden has read the letter.
Griner's representatives shared parts of the letter Monday.
"As I sit here in a Russian prison, alone with my thoughts and without the protection of my wife, family, friends, Olympic jersey, or any accomplishments, I'm terrified I might be here forever," Griner wrote.
The White House said Wednesday that Biden and Vice President Kamala Harris spoke with the detained basketball player's wife, Cherelle Griner, to assure her the administration is working to secure her release as soon as possible.
Russian officials have maintained a hard line toward Griner.
Foreign Ministry spokesman Alexei Zaitsev said Wednesday that the U.S. is attempting to misrepresent the case "as if the American was detained illegally," calling it a "serious offense" backed by evidence.
In a tweet, U.S. Secretary of State Antony Blinken said officials with the U.S Embassy in Moscow attended Griner's trial and delivered a letter from the president.
"We will not relent until Brittney, Paul Whelan, and all other wrongfully detained Americans are reunited with their loved ones," he added.
Griner is due back in court on July 14.
Some information for this report came from The Associated Press, Agence France-Presse and Reuters.