In addition to developing its own missiles, South Korea is now protected from a North Korean missile strike by a U.S. THAAD (Terminal High Altitude Area Defense) missile battery, which was brought into the country in March and deployed in the southeast.
Until then, the South had been barred from deploying ballistic missiles with a range of more than 300 kilometers, or 186 miles, and a payload of more than half a ton because of concerns about a regional arms race.
Another US official was quoted as saying that increased activity was detected at North Korea's sole nuclear test site in recent days.
Defence officials believe the missile may go up to 497 miles (800 kilometres) - the maximum ballistic missile range allowed under a deal with the United States - before it hit a designated test target.
The US official confirmed to AFP that Pyongyang tested a rocket engine on Thursday, on condition of anonymity and without providing further details.
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A series of tests that it has conducted have raised fears that it is bolstering its capabilities to strike South Korea, Japan and American military bases in the Western Pacific.
China's top diplomat, Yang Jiechi, told Trump in a meeting at the White House that Beijing was willing to "maintain communication and coordination" with the United States in an effort to defuse tension on the Korean peninsula, according to a statement from China's Foreign Ministry on Friday.
Any military solution to the North Korea crisis would be "tragic on an unbelievable scale", Trump's defense secretary, Jim Mattis, said last month.
Outside observers say Pyongyang's space programme is a fig leaf for weapons tests.
South Korea considered sharing some events at the Seoul 1988 Olympics with the North, but talks broke down and the North boycotted the Games.