Regarding the agreement, Kremlin spokesman Dmirty Peskov said, "No one has any right to criticize Russia and Turkey" for military and technical cooperation, which is "in strict compliance with international law and is in no way aimed against any third-party countries."
The total cost of the S-400 deal is believed to be around $2.5 billion.
Turkey's need for an air missile defense system became more urgent in the context of the ongoing civil war in Syria, where the Bashar Assad regime has a sizeable stockpile of ballistic missiles that threaten Turkey, as well as biological and chemical weapons.
In 2013, Turkey selected the China Precision Machinery Import-Export Corporation for procurement of a long-range air defense system but later scrapped the deal amid pressure from NATO.
The two leaders are also expected to discuss the cease-fire agreement brokered by Turkey, Iran and Russia at Astana in late 2016 amid efforts to reach a permanent solution to the Syrian civil war.
During the last two Astana meetings, de-escalation zones were established in order to end the conflict between opposition groups and the Syrian regime.
Last week, President Erdoğan said that Turkey will deploy troops to Idlib as part of a cease-fire agreement.
"The de-escalation zone agreement was a promising idea. …under which the Russians are maintaining security outside of Idlib and Turkey is maintaining security inside the Idlib region," Erdoğan said.
The latest developments regarding the Kurdistan Regional Government (KRG) were also addressed in the meeting, as both countries previously emphasized the importance of the territorial integrity of Iraq.
Russian-Turkish relations saw a quick recovery in terms of trade following the crisis that erupted after Turkey shot down a Russian warplane in November 2015.
Putin agreed to lift nearly all sanctions imposed on Turkish services, products, textiles and the construction sector during their last meeting in Sochi on May 3.