Noor in a statment said the two sides held talks regarding the bilateral relations between Kabul and Moscow, bilateral trade ties, joint fight against terrorism, and other key issues of bilateral interest.
He did not disclose further information regarding his meeting with the Ambassador of Russia in Kabul.
The meeting between Noor and the Russian Ambassador takes place at a time when Moscow is facing growing criticisms regarding its alleged support to the Taliban group.
The Afghan and American officials have long been claiming that Moscow has stepped up support to the Taliban group, a claim which the Russian officials have rejected.
The Commander of the NATO-led Resolute Support Mission in Afghanistan Gen. John Nicholson had also said earlier that both Russia and Iran are supporting the Taliban group.
On the other hand, Noor has stepped up his political efforts during the recent months as less than three months are left for the parliamentary and districts councils elections.
He announced the formation of the Grand National Coalition of Afghanistan during a gathering in Kabul nearly two weeks ago.