Russian gas monopoly Gazprom in January resumed imports of natural gas from Turkmenistan. The company in 2009 halted imports after an explosion on a Turkmen pipeline and declining European demand during the economic recession.
Ashgabat blamed Gazprom for the blast and has since moved to diversify its export options to European and Asian markets. The country said in September it was keen to send its gas through the planned Nabucco pipeline for Europe.
The Kremlin said imports approached 280 billion cubic feet of natural gas from Turkmenistan so far this year, the Bloomberg news agency reports.
Medvedev visited Friday with his Turkmen counterpart Gurbanguly Berdimuhamedov for an official state visit to discuss trade and energy issues.
"I am convinced the visit will be interesting and productive," the Russian president was quoted by state-run news agency RIA Novosti as saying.
Moscow said last week it started operating a $176 million gas pipeline in Turkmenistan. Trade between the two countries passed $1 billion in 2009 excluding gas deliveries.