A Soyuz-U launch vehicle carrying the space freighter blasted off from Baikonur at 00:45 a.m. Moscow time [20:45 GMT on Saturday].
"The docking was carried out in automated regime as scheduled,” a Roscosmos spokesman said.
Progress M-20M delivers some 2.4 metric tons of fuel, food, oxygen, scientific and medical equipment to the orbital outpost, which currently hosts three Russian cosmonauts, two NASA and one Italian astronauts.
Progress M-20M returned to the "short" six-hour flight path to the ISS. Previously, the Progress M-19M cargo spacecraft, launched in April 2013, reached the orbital outpost two days after liftoff.
Before that, three space freighters - Progress M-16M, Progress M-17M and Progress M-18M - also delivered their cargo to the ISS in six hours.
With a record of more than 130 launches since 1972 and only one failure, Progress-family freighters remain the backbone of the Russian space cargo fleet. In addition to their main mission as cargo spacecraft, they are used to adjust the ISS's orbit and conduct scientific experiments.