Leader Kim Jong-un declared the test "a new birth" for the North's rocket industry, state news agency KCNA said.He said the engine would help North Korea achieve world-class satellite launch capability, it added.
The development, not confirmed elsewhere, comes as US Secretary of State Rex Tillerson visits China - Pyongyang's main ally.
After personally overseeing the test, Mr Kim "emphasised that the world will soon witness the great significance of the epoch-making victory we achieved today", KCNA reported, adding that it marked the birth of the country's rocket industry.
Mr Tillerson's East Asian tour has been dominated by anxieties over North Korea's nuclear capabilities.
In South Korea on Friday, he said a US military response would be on the table if North Korea threatened South Korea or US forces.
The US and China pledged to work together to get the North to take "a different course" and move away from its weapons programmes after Mr Tillerson met his Chinese counterpart on Saturday.
The BBC's China editor Carrie Gracie says the North Korean announcement upstaged Mr Tillerson's subsequent talks with the Chinese President, Xi Jinping.
Kim Jong-un has said the country is close to a test-launch of an intercontinental ballistic missile.