In a phone call, Trump gave "conceptual approval" to a multi-billion dollar equipment sale to Seoul, the White House said in a statement, The Hill reported.
South Korea wants to increase its missile payload to one ton from the current 500 kilograms to better counter North Korea's missile capabilities.
Kim's neighbour is taking no chances as they begin to develop plans to kill or capture North Korea's leadership if the rogue state "crosses the line".
Park Soo-hyun, the spokesman for Seoul's presidential office, said the leaders had reached an agreement in principle to loosen - "to the extent hoped by the South Korean side" - limits on the South's ballistic missile capability.
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"Trump and Moon pledged to continue to apply strong diplomatic and economic pressure on North Korea and to make all necessary preparations to deter and defend against the growing threat posed by North Korea", it said.
South Korea's development of its ballistic missiles is limited to range of 800 km (500 miles) and payload weight of 500 kg (1,100 pounds) under a bilateral treaty revised in 2012.
The latest step comes after a roller-coaster month of escalating tensions over North Korea.
It came as US and South Korean forces were nearing the end of the 10-day annual Ulchi Freedom Guardian joint exercises, which the North regards as a rehearsal for invasion. They also agreed to update the missile guidelines.
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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.
Allowing South Korea more powerful weaponry signals to the North that Seoul will not necessarily be constrained by the United States and that it has an independent ability to react, Schuster said. President Moon denounced North Korea's recent missile launch over Japan.
Since 2008, photographer Eric Lafforgue ventured to North Korea six times. At the earlier meeting, held on July 7 on the sidelines of the Group of 20 Summit in Germany, the two had agreed on the need to bring North Korea back to denuclearization talks, with Putin saying Moscow does not recognize Pyongyang as a nuclear state. "There's no change", said an official from the Ministry of Trade, Industry and Energy. "Korea trade pact a truly bad idea", said foreign policy expert Richard Haass, who argued it would weaken the US alliance with South Korea at a crucial time.
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Incidents of Myanmar forces opening fire on Rohingyas gathered near the border have been reported in the last two days. According to the United Nations, more than 80,000 Rohingya have fled to Bangladesh since last October's clashes.