Alla Bout arrived in the United States with her daughter on Monday and will stay in the country for six weeks.
According to Antonov, Bout’s meeting with his family is planned for Thursday.
"As for our embassy, we will do everything possible so that the family reunites as soon as possible. We insist that Viktor Bout is released. We view the arrival of Bout’s family in the United States as an intermediate step," the Russian Ambassador told reporters.
Antonov said that Bout’s wife and daughter will have the opportunity to see each other four times during the week.
"At this stage it is the maximum that we have achieved," the ambassador said, stressing that the Russian diplomatic mission will continue to support Bout until his release.
Antonov called on rights groups both in the United States and Russia to pay more attention to Bout’s situation and to turn their eye on "other Russians, who have unjustly ended up in American prisons."
Alla Bout told reporters on Monday that the US State Department had given the green light to two additional meetings between Bout and his family.
On Tuesday, Alla Bout said that US authorities had refused to exchange her husband for American citizens imprisoned in Russia.
Bout was arrested in Bangkok in 2008. Two years later he was extradited to the United States, where he faced charges of conspiring to kill American nationals and of supplying Colombian rebels with weapons. Bout is now serving a 25-year sentence at the Marion federal prison in Illinois.