Prospects for talks on family reunions are less good because North Korea has previously demanded that South Korea repatriate some North Korean defectors living in the South before any reunions take place, according to the analysts.
"The elephant in the room is going to continue to be North Korea", Petraeus, 64, said in an interview Monday in Boston.
China National Petroleum Corp (CNPC), a state-controlled company, halted diesel and gasoline sales to North Korea "over the last month or two", amid global pressure on Pyongyang to curb its nuclear and missile programmes, Reuters exclusively reported on June 28.
South Korea on Monday offered talks with North Korea to ease animosities along their tense border and resume reunions of families separated by their war in the 1950s.
"Talks and cooperation between the two Koreas to ease tension and bring about peace on the Korean peninsula will be instrumental for pushing forth a mutual, virtuous cycle for inter-Korea relations and North Korea's nuclear problem", said South Korean Unification Minister Cho Myoung-gyon, as quoted by Reuters.
But analysts say North Korea may accept the defense talks because it wants the South Korean army to halt loudspeaker broadcasts at the border that began after North Korea's fourth nuclear test in January 2016.
According to Reuters, Chinese state-owned oil major CNPC has suspended diesel and gasoline sales to North Korea during the last month or two.
The United States, South Korea's main ally, which has been trying to rally worldwide support for tougher sanctions on North Korea, appeared cool to the proposal, recalling President Donald Trump's statements that conditions must be right for dialogue.More news: Shikhar Dhawan replaces injured Murali Vijay for Test series in Sri Lanka
In August 2015, North Korea's No. 2 leader, Hwang Pyong So, and South Korea's national security director, Kim Kwan-jin, met at Panmunjom and reached a deal on averting possible bloodshed over a land-mine blast that maimed two South Korean soldiers.
The Red Cross and the government have also proposed a separate meeting, aimed at discussing how to hold reunions of families separated by the Korean War, which ended in 1953.
"After North Korea's frequent missile tests including its very first ICBM test, the worldwide community has vowed to tighten sanctions, and China simply can not exclude itself from the recent movement, although it probably does not want to indefinitely cut off fuel sales to the North", Kang said.
The last such reunions were in October 2015.
President Moon Jae-in's overture Monday clearly showed again that he prefers diplomacy over pressure or economic sanctions to try to improve ties between the two Koreas and persuade the North to give up its nuclear weapons program. The ministry also did not elaborate what it meant by hostile military activities. -South Korea military drills.
Yonhap suggests the offer might have been made sooner if North Korea did not insist on proceeding with provocative missile tests.
Previously, Pyongyang has repeatedly said it refuses to engage in all talks with the South unless Seoul turns over 12 waitresses who defected to the South past year.