Bout was handed a 25-year prison sentence on Thursday after being found guilty of conspiring to sell arms to anti-US guerrillas in Colombia and to kill American service personnel.
The United States arrested him in Thailand after a tape-recorded sting operation and extradited him for trial in 2010.
But Russia has consistently denounced the case against the 45-year-old and said after the verdict it would make every "possible effort to return Viktor Bout to the Motherland," reiterating a call made after his November conviction.
"The Russian foreign ministry views the US court verdict sentencing Viktor Bout to 25 years in prison as baseless and biased," said a ministry statement.
Bout inspired the arms smuggler played by Nicolas Cage in the 2005 "Lord of War" movie, although in that film the hero ultimately went free after being detained by US authorities.
The ministry condemned the jury trial, saying it relied on "shaky evidence", and accused the US justice system of carrying out a "clear political order."
It also said that Bout's case would "remain among our priorities on the Russian-US agenda."
Foreign Minister Sergei Lavrov vowed he would "undoubtedly" discuss the case with US Secretary of State Hillary Clinton and described the verdict as "unwarranted".
Russia and US relations are going through a rocky period at the moment.
US Ambassador Michael McFaul has been targeted for his meetings with opposition leaders and he angrily called Russia a "wild country" in an encounter last week with a television crew.
The head of the lower house of parliament's foreign affairs committee, Alexei Pushkov, said Bout's fate would darken relations between the countries.
"Unfortunately Viktor Bout's sentencing along with other conflict situations create an unfavourable background for a new stage in Russian-US relations," he told Interfax.
But speaking to reporters in the Kazakh capital Astana, Lavrov appeared to soften Russia's rhetoric against the United States by saying that Moscow was not looking for revenge against Washington.
"We do not want revenge but to help Viktor Bout," said Lavrov, confirming that while Russia would support his appeal its ultimate aim was to bring Bout home.
Bout's case has drawn widespread public sympathy in Russia and his conviction and sentencing will have an ongoing effect, said Dmitry Trenin, director of the Carnegie Moscow Centre.
"I think it will weigh down relations," he told AFP.
"I don't think it will be a major stumbling block, of course not, but it is one of those things that will create an atmosphere.
"Here in Russia, in the government circles and in the public, the case is seen as unjust."
Lavrov vowed to keep up pressure of the United States over Bout's case and said Moscow would "actively support" an appeal announced by his lawyers and fight for his return to Russia.
"In any case we will work to return him to his motherland. We have the legal instruments to do this with the United States," he said, without using the word extradition.
The justice ministry said earlier Bout's handover to Russia was possible on the basis of the Convention on the Transfer of Sentenced Persons, a treaty drawn up by the Council of Europe to which Moscow and Washington are parties.
Bout's wife Alla on Friday urged Russia to obtain Bout's handover.
"Russia must express a more harsh position on this question. There must be concrete action to return Viktor Bout to his Motherland," she told Interfax.