The unmanned Progress M-23M ship, which was launched from the Baikonur cosmodrome in Kazakhstan yesterday, docked with the ISS at 2114 GMT, two minutes later than scheduled, the Roscosmos agency said.
The station was flying over the west coast of Peru at the time, NASA said.
The ship is packed with some 2.4 tonnes of supplies for the station's six-member international crew, including fuel, water, oxygen, and parcels from friends and family.
The ISS is currently under the command of Koichi Wakata, the first Japanese astronaut to hold the post. Also on board are Russian cosmonauts Alexander Skvortsov, Oleg Artemyev, and Mikhail Tyurin, along with Americans Steve Swanson and Richard Mastracchio.
Roscosmos deputy Denis Lyskov said this week that Roscosmos was not planning any retaliatory measures.
NASA has been wholly reliant on Russia for delivering astronauts to the space station since the US retired its space shuttles in 2011.