The hearing, which was adjourned to 29 July, was held on Wednesday behind closed doors at the request of defence lawyer Muhsin Dhiab al-Suwaidi who cited "the confidentiality of information" linked to the process.
Al-Suwaidi told reporters after the one-hour session - held under tight security - that he had explained to judge Abd Allah al-Saadi "the reasons for submitting the appeal".
Anatoly Bilashkov and Vassily Pokchov were jailed last month for 25 years, equivalent to a life term in Qatar, for the 13 February killing of Zelimkhan Yandarbiyev, a former Chechen president who lived in Doha.
Judge Ibrahim Salih al-Nisf said then the court had been lenient in not sentencing the pair to death, as the prosecution had sought, and mentioned that the "Russian leadership" had ordered the killing.
Moscow has insisted the two are innocent.
Both men had pleaded not guilty to the car bombing after the Friday prayers that killed Yandarbiyev and wounded his 13-year-old son.
The murder sparked a diplomatic row between the Gulf state and Russia.
Yandarbiyev, who briefly headed the war-torn republic of Chechnya in the mid-1990s, had lived in Qatar for nearly three years with his family.