The rocket blasted off at 3:03 a.m. Moscow time (00:03 GMT) from the Baikonur space center in Kazakhstan and put the satellites into orbit as previously scheduled at 12:29 p.m. (09:29 GMT).
Anatoly Shilov, the head of Roscomos Space Communication and Ground Control Complexes department, said that "the task of putting the satellites into orbit has been accomplished."
He also said the simultaneous orbiting by Proton of two satellites of this type was an historic event. The total weight of the two satellites is 3,700 kg (8.114 lbs).
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.
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.