"Both sides have expressed confidence that Russian-Turkmen relations will continue to advance in all areas, including energy, which is so important for the two States," the service said.
It said Putin and Berdymukhammedov, in a telephone conversation, wished each other a happy New Year, as well as stability, peace and prosperity to the people of Turkmenistan and Russia.
Turkmenistan's acting President Gurbanguly Berdymukhammedov was approved as presidential candidate by the Central Asian state's top legislative body Tuesday along with five other contenders.
Berdymukhammedov, 49, deputy prime minister since 2001, tops the list of six candidates approved by the People's Council and selected out of 11 nominees to run for president of the gas-rich country and replace the long-time ruler Saparmurat Niyazov, who died of heart failure last week.
Berdymukhammedov is seen by analysts as the most likely successor to the post, although the Constitution bars an acting president from running for elections.
The council decided Tuesday that the presidential election will be held February 11.