Vice Defense Minister Suh Choo Suk said the South's defense officials are proposing talks at the border village of Panmunjom on Friday to discuss how to end hostile activities along the border. The last such talks were held in December 2015.
European Union sanctions against North Korea date back to 2006 and are part of global efforts to halt a nuclear and ballistic missile programme that experts say is meant to give Pyongyang the capability to hit the USA mainland.
The American news agency cited a human rights organization based in South Korea, which claims that there are about 50,000 North Koreans in Russian Federation who are being exploited by their government.
The Trump administration angered China last month by imposing sanctions on a Chinese bank accused of laundering North Korean cash and approving a $1.3 billion arms sale to Taiwan, which Beijing considers a breakaway province.
Last year, China shipped more than 96,000 tons of gasoline and almost 45,000 tons of diesel to the isolated communist state, worth a combined $64 million.
Those talks would be held on August 1, also in Panmunjom - that is, if Pyongyang accepts.
China's foreign ministry welcomed Seoul's peace gesture, saying it hopes "the two sides will move in a positive direction to. break up the stalemate and to relaunch the dialogue and negotiations".
The latest ICBM test - which Kim described as a "gift" to the Americans - was seen as a milestone in Pyongyang's quest to build a missile capable of carrying a nuclear warhead that can hit the U.S. mainland.
If the talks are held, loudspeaker broadcasts, leafleting and South Korea-U.S. drills are expected to top the agenda.
Moon, who took power in May, has advocated dialogue with the nuclear-armed North to bring it to the negotiating table and vowed to play a more active role in global efforts to tame the South's unpredictable neighbour.
Stopping hostile acts along the MDL that escalate military tensions can be a first and meaningful step, as Korea marks the 64th anniversary of the Armistice Agreement on July 27, he added. Since no truce was agreed, the two sides remain technically at war.
South Korea offered Monday to talk with North Korea to ease animosities along their tense border and resume reunions of families separated by their war in the 1950s.
North Korea's state media hasn't immediately responded to South Korea's overtures.
North Korea says the South abducted the 12 waitresses and the restaurant manager and has demanded their return, but the South has said the group made a decision to defect of its own free will. Cho said this matter is not included on the talks agenda.
The government is likely North Korea's largest user of fuel products, but most gasoline and diesel bought by ordinary citizens comes from private dealers and smugglers, experts say.