The first Angara will be sent to the Plesetsk space centre in northern Russia later this month, the manufacturer said in a statement, but did not give a precise launch date.
Meanwhile, the first heavy-class Angara-A5 has been completed and will soon be presented to the public, a Khrunichev spokesman said.
The project is being personally overseen by Defence Minister Sergei Shoigu and Deputy Prime Minister Dmitry Rogozin, who is in charge of the defense industry.
Deputy Defence Minister Yury Borisov said earlier in May that the light-class Angara would be launched in mid-2014 and its heavy variant towards the end of this year.
The light-class Angara was initially due to be launched in 2013.
Deputy Defence Minister Col Gen Oleg Ostapenko said in April that the new rocket would only be launched after the construction of a new launch facility at the Plesetsk space centre is completed.
The Angara family of rockets, designed to provide lifting capabilities of between 2,000 and 40,500 kg into low earth orbit, has been in development since 1995.
The rocket has a liquid-oxygen and kerosene powered first stage and hydrogen-oxygen fuelled second stage.
The rockets have a modular design similar to the US-made Evolved Expendable Launch Vehicle (EELV), based on a common Universal Rocket Module (URM).
Angara rockets will reduce Russia's dependence on the Baikonur space centre which it leases from Kazakhstan, by allowing the launch of heavy payloads from Plesetsk and from the new Vostochny space centre in Russia's far east.