But some critics have raised questions over the effectiveness of the restrictions, as North Korea is still able to trade internationally.
South Korea offered humanitarian assistance to the North even under conservative administrations, but Moon's predecessor under an ousted President Park Geun-hye held off the aid after the North's fourth nuclear test in January 2016.
The effectiveness of the sanctions depends largely on whether China, North Korea's ally and main economic partner, will fully implement them.
During the mission, the aircraft from the United States and South Korea practised their attack capabilities by releasing live weapons at the Pilsung Range training area. One critic tells VOA that Pyongyang will divert at least 30% of food aid "to the military or the elite".
The U.S. military has described the exercises as training for readiness "to fight tonight" against North Korea if needed.
Mattis explained the recent threats by North Korea and how the USA will deal with the alleged threats to them and their allies.
"The two leaders agreed to work closely and to put stronger and more effective sanctions and pressure on North Korea in cooperation with the worldwide community", South Korea's presidential spokesman Park Soo-hyun said. Trump is due to discuss the issue with Japanese Prime Minister Shinzo Abe and South Korean President Moon Jae Inn on Thursday.
The Chinese and Russian foreign ministers called for a peaceful end to the "vicious cycle" on the Korean peninsula as they met in NY for the UN General Assembly, Beijing said Tuesday.
Trump's speech "reaffirmed that North Korea should be made to realize denuclearisation is the only way to the future through utmost sanctions and pressure", it added.
According to Reuters, the ships sailed from Russian Federation, either the port of Vladivostok or Nakhodka, and registered either China or South Korea as their destination with the appropriate authorities.
It is the 14th ballistic missile launch by North Korea this year. "We're not giving up on diplomatic efforts", she said.
North Korean rhetoric never threatens a gratuitous attack upon the USA or its allies, but rather a fierce rejoinder should their country be attacked. The move, which runs contrary to American and Japanese calls for an increase in economic and diplomatic pressure, marks a resumption in South Korean aid after a break of nearly two years.
On Tuesday, US President Donald Trump warned North Korea in his speech to the United Nations that the US would "totally destroy" the country if threatened.
North Korea last week fired a missile that flew over Hokkaido in northern Japan and landed in the Pacific Ocean. Trump said on Friday he was "more confident than ever that our options in addressing this threat are both effective and overwhelming".