Rear Admiral Ali Shamkhani said the test carried out on Sunday was: "100% successful."
Military experts believe the test, if true, was important for two reasons.
First, in order to develop a missile with a range greater than 2000km - in effect a two-stage rocket - a country needs to master the more complex solid fuel technology. This is because solid fuel is more stable inside the missile.
Second, solid fuel missiles of all ranges are more mobile and can be deployed far more quickly than liquid-fuel devices, which need to be filled up immediately before they are launched.
Iran has recently upgraded the Shahab-3 ballistic missile, believed to be based on a North Korean design, to have a range of what it says is at least 2000km – putting Israel and US bases in the region well within range.
The Shahab-3 is based on liquid-fuel technology.
Tehran's rapid progress on its ballistic missile programme is a major cause for concern among the international community, particularly Israel, which is already alarmed over Iran's nuclear activities.
Iran insists it is not seeking to develop missiles with a longer range, and has denied allegations that it is seeking to develop nuclear weapons. The country says its missiles will only be tipped with conventional warheads.