Country leader Kim Jong Un said the successful test was "a new birth" of its rocket industry.
The new engine is an ambitious development with regards to North Korea's long-range missiles.
Mr Kim said the "whole world will soon witness what eventful significance the great victory won today carries".
The KCNA said he checked the technical specifications of the engine and preparations for the test, and gave appropriate instructions before going up to the observation post to give the order for the test to begin.
U.S. Secretary of State Rex Tillerson has been in China over the weekend on the last stop of a three-nation tour of Northeast Asia.
"So I hope the North Koreans can assist us in solving the murder case of Kim Jong-nam", Khalid added.
The KCNA added that the test confirmed the engine's qualifications, saying it proved "stable maintenance of indices of all systems such as starting and stopping features" of the high-powered engine, which it called a "Korean-style" incorporation of "indigenous technology".
The report marks the latest challenge to the United States from Kim's defiant regime.
Hai Ram! Yogi Adityanath is the chief minister of Uttar Pradesh
Of the 47 ministers in the state, 26 hail from upper castes, three ministers are Dalits and the rest belong to Backward Classes. Baldev Singh Aulakh, a Sikh, who got elected from Bilaspur also took oath as minister of state.
"The rail-mounted environmental shelter has been moved up against the engine test stand since February 5, either for maintenance or to position a rocket engine for testing", 38 North said in a note.
United States president Donald Trump's new right hand man Rex Tillerson met with his Chinese counterpart on Saturday.
He said that investigators were looking to detain at least one "important" person, but did not elaborate on whether any North Koreans were among the people being pursued.
The test site is close to where North Korea launched four extended-range Scud missiles into the Sea of Japan earlier this month.
In his New Year address, Kim Jong-un said his country's ICBM development program was "at its final phase", raising the prospect of the North's firing an ICBM missile this year. "China has done little to help!"
During diplomatic meetings in Japan and South Korea this week, Tillerson called for tougher sanctions on Pyongyang and said the USA would not rule out military action against the country.
In a total switch from previous policy, Mr Tillerson said: "Let me be very clear: the policy of strategic patience has ended".
Kim has said he's close to developing an intercontinental ballistic missile capable of reaching North America.