A court in Hungary ruled on Wednesday that Irina Belenkaya should remain in police detention until an extradition request from the French authorities on kidnapping charges is issued.
However, if France fails to issue an extradition warrant within 40 days, Belenkaya, who refused to consent to the simplified extradition procedure, will be freed.
"We believe that the court approached this case in a highly responsible manner, without bias, and took into consideration all of the complicated factors involved," ministry spokesman Andrei Nesterenko said.
Nesterenko said France has agreed to a Russian Foreign Ministry proposal to hold talks on the case.
"We do not deny that we are glad about this," he said. He also said the ministry hopes the father of Elise Andre withdraws his lawsuit against Belenkaya.
Belenkaya was arrested on Sunday night while trying to cross the Hungarian border into Ukraine with her three-year-old daughter, Elise Andre.
Elise, who was snatched from her father last month, returned to France on Tuesday along with her 51-year-old father, Jean-Michel Andre.
In France, Belenkaya is also accused of organizing an attack on the girl's father. Jean-Michel says his ex-wife was among a group of assailants who seized his daughter from him.
Jean-Michel told RIA Novosti on Wednesday that he did not want his wife to face a jail term for kidnapping her child and agreed to send his daughter to Russia for two months if her return back to France was guaranteed.
Elise has been "kidnapped" back and forth three times in the past two years by her warring parents. Andre, who was awarded custody by a French court after their divorce in 2007, is wanted in Russia, where Belenkaya has been granted custody of the girl.