"Any effort by the Government of the Republic of Turkey to further enhance their relationship with Russia will degrade the general security of the NATO alliance."
The Justice and Development party's deputy chairman says Russia is also complicit.
The Kremlin is aware of Erdogan's request to meet but would not accept or decline it.
Rosturizm has told tourists to take all necessary safety precautions while visiting Turkey.
The move will create 87,000 new jobs for Russians, according to the president.
The group posted pictures of the Turkish flag and Mustafa Kemal Atatürk.
The three Russian nationals are among more than 60 people detained by Turkish authorities following Tuesday's deadly bombing in Istanbul
Research shows a shift in coverage following Turkey's downing of a Russian jet.
The Russian President made the comments during a live broadcast of his state of the nation address
Other industries wait for Russia's next move in the ongoing row.
Russia says one of the jet's pilots was killed but the other is safe