Erdogan's request followed two days of talks in Ankara with Russian officials about how the two regional powers intend to jointly implement a Russian-brokered ceasefire signed last week.
Turkey is one of Azerbaijan's closest allies and has strongly defended its right to reclaim lands it lost to ethnic Armenian separatists in a 1988-94 war.
The Russia-brokered deal brought an end to more than six weeks of fighting that claimed more than 1,400 lives and saw ethnic Armenians to agree to withdraw from large parts of the contested region of Azerbaijan.
Erdogan asked parliament Monday to deploy a mission to "establish a joint centre with Russia and to carry out the centre's activities".
The deployment would be active for one year and its size determined by Erdogan.
Russia is sending 1,960 peacekeepers as well as armoured personnel carriers and other military equipment to monitor the truce deal.
Moscow has stressed repeatedly that Turkey will have no troops on the ground under the truce deal's terms.
The Russian-brokered agreement states that a "peacekeeping centre is being deployed to control the ceasefire" but does not specify its formal role.
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