The move could give South Korea more independence from the United States to react to the threat from North Korea, analysts say.
The two leaders spoke in a phone call Friday.
"President Moon and President Trump reaffirmed their view that it is important to apply maximum sanctions and pressure on North Korea so that it refrains from making provocations and comes out to the dialogue table to peacefully resolve its nuclear issue," presidential spokesman Park Soo-hyun said in a written statement.
According to the statement, the two also agreed "in principle on the revision of the missile guidelines."
"Sharing the view that South Korea needs to bolster its defense capabilities to counter North Korea's provocations and threats, the two leaders agreed in principle to revise the missile guidelines to a level that the South Korean side desires," the spokesman's statement said. It did not provide further details about what the revision would entail.
Under the bilateral pact last revised in 2012, South Korea is allowed to develop ballistic missiles with a range of up to 800 kilometers (500 miles) and a payload weight of up to 500 kilograms (1,100 pounds).
The White House said Trump gave Moon his "conceptual approval" for the planned purchase by Seoul of billions of dollars of US military equipment.
The latest step comes after a roller-coaster month of escalating tensions over North Korea. Trump's suggestion this week that action, rather than talk
, is needed to deal with Pyongyang has seemed to contradict some of his top Cabinet officials, who insist the United States will continue to seek a peaceful resolution despite the reclusive state's provocative missile tests.
Analyst: Boost to South Korean confidence
Carl Schuster, a former director of operations at the US Pacific Command's Joint Intelligence Center, told CNN that revising the bilateral treaty would give the South Koreans a more independent deterrent capability, which they have wanted for years.
"The reason they want it, I think, is they want to be able to either respond to North Korean provocation or they want North Korea to be aware that they have the capability to respond if North Korea goes too far," said Schuster, now a Hawaii Pacific University professor.
"To an extent it's as much a political as an operational development that's important to South Korean self-confidence."
Moon has sought to be "more accommodating" to North Korea than his predecessor and looked for nonmilitary ways to resolve the situation, Schuster said, but the North's recent actions have undermined public confidence in his policies.
They have also alarmed South Korea's allies in the region and around the world.
The United States responded this week to a series of missiles launches by North Korea -- one of them over Japan -- by staging a mock bombing drill
with South Korea over the Korean Peninsula. South Korea also held a live-fire drill simulating the destruction of North Korea's leadership.
Pressure on China?
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.
The shift in tack could reflect Trump's belief that it's time to try something new and his desire for China to do more to rein in North Korea, the professor said.
In the 1990s, US 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. However, this approach clearly hasn't worked.
Allowing South Korea to have longer range missiles could put pressure on China to exert influence over North Korea, Schuster said, because the Chinese will see that as creating a potential threat to them, too.
North Korea: 'Recognize our nuclear program'
Meanwhile, commentary Friday in the Rodong Sinmun newspaper, the official mouthpiece of North Korea's Workers' Party of Korea, called on the United States to recognize the North as a nuclear power if it wants future diplomatic efforts to make headway.
"The situation is turning unfavorable for the US day by day. There is no proper way out. The US. should make a switchover in its policy on the basis of recognizing the fundamentally changed DPRK strategic position and geographical influence," it said, using an acronym for the Democratic People's Republic of Korea.
"As the US escalates the confrontation with the DPRK and wastes time to find out a solution, the striking capabilities of the DPRK's strategic forces which put the whole US mainland in their strike range will rapidly increase."
A day earlier, Russian President Vladimir Putin warned the United States and others against going down a "dead-end road"
on North Korea and called for talks to resolve the issue, saying "putting pressure on Pyongyang to stop its nuclear missile program is misguided and futile."