Decision announced after phone call between US President Donald Trump and his South Korean counterpart, Moon Jae-in.
A US official who studies North Korea's military and politics said it was too early to determine if the test supported the North's claim that it had succeeded in developing a thermonuclear weapon, "much less one that could be mounted on an ICBM and re-enter Earth's atmosphere without burning up".
White House press secretary Sarah Huckabee Sanders denied there was any inconsistency in Trump's remarks. And we're continuing to move forward on that. President Moon denounced North Korea's recent missile launch over Japan.
"Mr. Trump is not a model of consistency, so I wouldn't read too much" into what he tweeted and what he reportedly agreed upon with Moon, said Sue Mi Terry, formerly a Central Intelligence Agency analyst and National Security Council director for Korea and Japan.
"The two leaders agreed to the principle of revising the missile guideline to a level desired by South Korea, sharing the view that it was necessary to strengthen South Korea's defense capabilities in response to North Korea's provocations and threats", South Korea's presidential Blue House said.
South Korea's development of its ballistic missiles is limited to range of 800 kilometres (500 miles) and payload weight of 500 kilograms (1,100 pounds) under a bilateral treaty revised in 2012.
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The warning comes just days after North Korea raised the stakes by firing an intermediate-range missile over Japan. The tested rocket was an intercontinental ballistic missile (ICBM).
North Korea on Thursday vowed to execute reporters from two South Korean newspapers, saying they insulted the country's dignity while reviewing and interviewing the British authors of a book about life in the isolated country.
Hours before the test, Trump had talked by phone with Japanese Prime Minister Shinzo Abe about the "escalating" nuclear crisis in the region. Japan also raised the prospect of further sanctions, saying curbs on North Korea's oil trade would be on the table.
North Korea has been working to develop a nuclear-tipped missile capable of hitting the United States and has recently threatened to land missiles near the U.S. Pacific territory of Guam.
A hydrogen bomb can achieve thousands of kilotons of explosive yield - massively more powerful than some 10 to 15 kilotons that North Korea's last nuclear test in September was estimated to have produced, similar to the bomb dropped on Hiroshima, Japan, in 1945.
A United States official who studies North Korea's military and politics said it was too early to determine if a test supported the North's claim that it has succeeded in developing a thermonuclear weapon, "much less one that could be mounted on an ICBM and re-enter Earth's atmosphere without burning up". "In any case, there is nothing wrong with talking as long as we don't make unilateral concessions".
"The reality is that talks with the North are unlikely to be successful, but the US hands Pyongyang an unearned public relations win if it simply dismisses talks out of hand", Terry, now managing director for Korea with the Bower Group, a government affairs and public policy consulting firm, told VOA.