Griner is charged with drug offenses and faces up to ten years in prison.
Griner's lawyers want to reduce the prison term if convicted.
They insist that the e-cigarettes were used for medical purposes and that Griner brought them along accidentally.
She was arrested on February 17 at a Moscow airport after having e-cigarettes with cannabis oil in her luggage.
A crime Griner pleaded guilty to.
In the United States, it is legal in some states to use cannabis for medical purposes - something it is not in Russia.
- We do not deny that Brittney brought it as medicine, but we believe that she brought it involuntarily because she was stressed when she packed, said one of Griner's lawyers Alexander Bojkov during Tuesday's trial, which continues on Wednesday.
"Must understand"
- The Russian people must understand that it is not used for recreational purposes.
It was prescribed by a doctor, he continued.
Spokespersons for US President Joe Biden have strongly questioned her imprisonment, saying she was "imprisoned on false grounds".
The Russian Foreign Ministry responded to the allegations last week.
"Feels well under the circumstances"
- If an American citizen was caught in connection with her smuggling of drugs, and she does not deny this, this should be proportionate to our Russian, local laws and not to those of San Francisco, New York and Washington, said the spokesperson Maria Zacharova .
- You see, if drugs are legalized in the United States, in a number of states, and this is done for a long time, so that the whole country will become addicted to drugs, it does not mean that all other countries follow the same path, she continued.
Griner has been in custody for over five months and a court has extended her detention until December 20.
During Tuesday's court hearing, Phoenix Mercury star Griner confirmed that she is fine under the circumstances, according to US diplomat Elizabeth Rood who was in court.
In an ABC interview during the day, Griner said she had nothing to complain about.