Berdymukhamedov gifted Putin the puppy in wake of latter's birthday.
The two leaders held talks in Sochi, on the sidelines of a summit of ex-Soviet states.
A video snippet showed an elated Putin, who is an avid dog lover, celebrating his 65th birthday on October 7, holding and kissing the dog, named Verny, meaning "Faithful" in Russian, during the meeting.
It was not the first time the Russian leader had been gifted animals.
Putin previously received a Bulgarian shepherd named Buffy from Bulgaria's premier and an Akita named Yume from a Japanese official.
The Russian leader has also been gifted horses and even a tiger.
According to reports, Berdymukhamedov is keen to recover lost Russian markets for Turkmen gas.
Russia, once the main buyer of Turkmen gas, stopped buying the fuel last year due to a price dispute.(ANI)