Azerbaijan and Armenia signed a Russia-brokered ceasefire on Nov. 10 that halted six weeks of clashes in the mountain enclave, which is internationally recognised as part of Azerbaijan but is mainly populated by ethnic Armenians.
Russian peacekeepers have been deployed in the enclave under the ceasefire deal, which locked in Azeri advances. Turkey has no peacekeepers there but has signed an agreement with Russia to set up a joint centre to monitor the ceasefire.
"We have the opportunity to develop and expand this more. We discussed these development and expansion efforts with Mr Putin too," Erdogan said.
He said the process of maintaining the ceasefire could be taken "to a different level" if other countries in the region were involved but did not name any in his public comments.
Turkey and Russia have been holding talks on the parameters of the monitoring centre, but a Turkish source told Reuters the two were at odds over Ankara's wish to set up an independent military observation post on Azeri territory.
Turkey has long backed its ethnic Turkic kin in Azerbaijan over Nagorno-Karabakh, and criticised the co-chairs of the so-called Minsk Group of the Organization for Security and Co-operation security and rights watchdog for not resolving the conflict in decades of mediation. The Minsk Group includes France, Russia and the United States.
France, whose population includes between 400,000 to 600,000 people of Armenian origin, wants international supervision of the ceasefire because of concerns that Russia and Turkey may cut Western powers out of future peace talks.
Erdogan said "discomfort" voiced over the agreement by some co-chairs of the Minsk Group "has no worth whatsoever."