The rockets can reach speeds of up to 7,680mph and travel more than 12,000km.
The practice sessions come after North Korea slammed Trump as a "mentally deranged dotard" on Saturday.
According to Reuters, "the number of sites that may ultimately be deployed had yet to be determined."
The land-based system can shoot down a missile both inside and just outside the atmosphere.
The two men met at the Asian Leaders Conference in the South Korean capital.
A suspected North Korean drone was found with photos of THAAD by South Korean military officials after it crashed near the nations' mutual border.
Sunday's test was detected by the U.S.-developed THAAD anti-missile system, despite much controversy surrounding its installation last month.
According to polls, liberal Moon Jae-in is likely to sweep to victory.
North Korea's state-run media outlet called on South Koreans to 'wage unflinching struggle' against the U.S.'s missile defense system.
Seoul now has an "early capability" to defend against North Korea's nuclear missile threat.
Trump's national security adviser, H.R. McMaster, reassured his South Korean counterpart, Kim Kwan-jin, that the U.S. alliance with South Korea was its top priority in the Asia-Pacific region.
President Donald Trump blasted the 'horrible' trade deal between the U.S. and South Korea, threatening to "terminate" it if Seoul didn't pay for the billion-dollar THAAD.
North Korea remained defiant and vowed to continue with nuclear and missile tests.
The U.S. military started moving parts of the THAAD missile system to a deployment site in South Korea on Wednesday.
The earlier-than-expected move was denounced by the frontrunner in South Korea's presidential election.
If Moon Jae-in, front-runner for the May 9 election, reverses policy on the deployment of the THAAD system, it will place him at odds with the United States, South Korea's biggest ally.
The U.S. started deploying its advanced anti-missile defense system in South Korea on Tuesday in response to North Korea's ballistic missile and nuclear tests.
China's foreign minister called on North Korea to halt nuclear activities and the U.S. to stop military drills.
China objects to the deployment in South Korea of the THAAD, as the radar is capable of penetrating Chinese territory.
The Russian president will welcome Park Geun-hye in Vladivostok.