The report is based on one training exercise carried out in Ukraine.
All five crew members are reported dead.
The Syrian Observatory for Human Rights calls on Moscow to cease killing of Syrian people.
The U.S. presidential hopeful blames Russia's lack of respect for President Barack Obama.
"People need to understand that this is serious business," the U.S. secretary of state said.
The remaining Russian forces will continue to hit ground targets in Syria.
The incident is the second crash during practice for the Russian air force this year.
Putin may have insisted on new Iranian forces before committing his air force.
Russia's ambassador to Denmark made the comments in an opinion piece published in a Danish national newspaper.
The decision means that almost half of the country's new fighter jets and helicopters will be stationed near Crimea.