Trump, who has warned that the USA military is "locked and loaded" in case of further North Korean provocation, reacted angrily to the latest missile test, declaring on Twitter that "talking is not the answer" to resolving the crisis.
US President Donald Trump and South Korean President Moon Jae-in said they plan to revise a 43-year-old joint treaty that caps the number and range of South's ballistic missiles, Moon's office said on Saturday.
They have also alarmed South Korea's allies in the region and around the world.
"The two leaders noted the need to strengthen the Republic of Korea's defense capabilities to counter provocations and threats from North Korea, and reached an agreement in principle to revise the "missile guideline" to the extent hoped by the South Korean side", South Korean news agency Yonhap quoted South Korean presidential spokesman Park Soo-hyun as saying.
South Korea's military says that it appears North Korea may have conducted its sixth nuclear test.
Under a bilateral agreement with the United States, Seoul is now restricted to ballistic missiles with a maximum range of 800 kilometres (500 miles) and payload of 500 kilogrammes (1100 pounds).
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It added that Trump provided his "conceptual approval" of South Korea's purchase of American military equipment worth billions of dollars, without adding further details.
Both the leaders have agreed during the conversation that South Korea's military arsenal would have to be strengthen in a bid to equip the nation better, to deal with the constant threat from Kim Jong Un-led North Korea. A day earlier, he had said "all options are on the table" following North Korea's Tuesday launch of a missile over Japan.
Since 2008, photographer Eric Lafforgue ventured to North Korea six times.
In the 1990s, United States policymakers were keen to constrain the offensive capabilities of countries in northern Asia because it was believed this would dissuade North Korea from increasing its own defensive capabilities, Schuster said. The Japanese leader also said he has ordered relevant ministries to gather and analyze information and inform the public appropriately.
Signed with the U.S. in 2001 - the year South Korea joined the MissileTechnology Control Regime (MTCR) - the agreement initially limited Seoul to rockets with a range of just 300 kilometres, due to United States concerns about triggering a regional arms race in Northeast Asia.