Lieutenant Colonel Alexei Zolotukhin said the German satellite would be orbited at 8:43 p.m. Moscow time (17:43 GMT).
The launch was originally scheduled for March 25, but was postponed twice due to bad weather.
The German SAR-Lupe satellite is designed to provide high-resolution radar images to NATO military commanders in Europe. It offers spatial resolution of less than 1 meter, and allows imaging at night and through clouds.
Russia's Space Forces previously conducted three SAR-Lupe launches in 2006-2007, under a 2003 contract between Russia's state arms exporter Rosoboronexport and German Cosmos International Satellitenstart Gmbh (a subsidiary of OHB Systems AG), which stipulates five SAR-Lupe launches until 2009.
The Cosmos 3M is a liquid-fueled two-stage rocket, first launched in 1967, with over 410 successful launches to date. The booster has been designed to lift a payload of up to 1,500 kg (3,300 lbs) into low, medium, and high orbits.