"We still expect the coalition forces [to take] decisive actions to track down those who killed our diplomats, as well as efficient measures to ensure the security of foreign nationals based there," said the source.
He said the coalition forces were responsible for maintaining security in Iraq under UN Security Council resolutions.
On Wednesday, President Vladimir Putin ordered special forces to "eliminate" the killers of the five Russian embassy employees in Iraq and called for international help in hunting the criminals down. An al-Qaeda-linked Islamist group had claimed responsibility for killing the diplomats, four of whom were kidnapped before being murdered.
Russia's lower house of parliament, the State Duma, passed a resolution Wednesday saying that the killings had been largely due to the coalition's lack of control over the situation in Iraq.