US reporter Evan Gershkovich appeared at a Moscow court on Tuesday, in the first partly open hearing since his arrest for alleged espionage, in a case that has drawn international condemnation.

Wearing jeans and a blue checked shirt, Gershkovich crossed his arms and smiled before the start of the appeal hearing against his pre-trial detention.

But, after a short hearing, his request for release on bail was turned down, with the judge saying his detention would "remain in place, without any changes".

"All understood. Thank you very much," Gershkovich was heard telling the judge from inside the defendant's glass cage.

Handcuff marks were visible on his hands.

"He has a fighting spirit. He's working out and he knows that people are supporting him," Maria Korchagina, one of his lawyers, told AFP after the hearing.

Speaking in English, she also told a group of reporters that Gershkovich "would like to prove that he is not guilty, he would like to prove there is a place for freedom of journalism".

His other lawyer, Tatyana Nozhkina, said Gershkovich was reading a lot in prison and was currently working through Leo Tolstoy's classic "War and Peace".

The lawyers said they had requested his release under house arrest and had offered to pay bail of 50 million rubles ($613,000).

US ambassador to Moscow Lynne Tracy was also present in the courtroom, although she was ushered out along with the press for most of the hearing.

The Wall Street Journal reporter, a US-born son of Soviet Jewish emigres, was arrested last month by Russia's FSB security service during a reporting trip in the Urals city of Yekaterinburg.

The FSB said the 31-year-old tried to obtain classified defence information for the US government, but the details of the case have been kept top secret.

Gershkovich has firmly rejected the charges, which carry a maximum sentence of 20 years in prison.

Any trial could be months away.

- 'Remains strong' -

Gershkovich, who has also worked for AFP, is the first foreign journalist arrested on spying allegations since the collapse of the Soviet Union.

Since his arrest on March 29, Gershkovich has appeared in court only once before -- at a closed custody hearing on March 30.

He was remanded in custody until May 29 and is being held at the Lefortovo prison in Moscow, where many high-profile prisoners accused of treason and espionage have been held.

"He is in good health and remains strong," US ambassador Tracy was quoted by the US embassy as saying after visiting him on Monday.

In his first contact with the outside world, Gershkovich wrote a handwritten letter to his parents in Russian. "I am not losing hope," it read.

His mother Ella Milman said he "felt it was his duty to report" from Russia.

"He loves Russian people," she said in a video interview with the Wall Street Journal.

US President Joe Biden has called his imprisonment "totally illegal".

More than three dozen news organisations have also signed a letter to the Russian ambassador in the United States, denouncing "unfounded espionage charges".

"Gershkovich's unwarranted and unjust arrest is a significant escalation in your government's anti-press actions," the letter released by the Committee to Protect Journalists said.

"Gershkovich is a journalist, not a spy, and should be released immediately and without conditions," it added.

The arrest has raised speculation that Russia may want a prisoner swap like the one last year in which Russia released US basketball star Brittney Griner, who had been arrested over traces of cannabis found in her possession.

She was exchanged for Viktor Bout, a Russian arms dealer imprisoned in the United States.