The rocket blasted off at 3:03 a.m. Moscow time (00:03 GMT) and is due to put the satellites into orbit at 12:29 p.m. (09:29 GMT).
The Express-AM44 and Express-MD1 satellites were built under the Russian Federal Space Program for 2006-2015.
The Express-AM44 will replace the Express-A3 satellite, which has reached the end of its service life, and the Express-MD1 will augment Russia's satellite network capacity in a key orbital position, the statement said.
Russia launched the first Express-series satellite, the Express-2, in October 1994 to boost the capacity of the country's satellite communications networks.
The Russian federal space agency, Roscosmos, is planning to carry out a total of 39 launches from the Baikonur and Plesetsk space centers this year. Russia rents Baikonur from Kazakhstan. The Plesetsk space center is in northwest Russia.
