China's President Xi Jinping arrives for the APEC Summit in Danang, Vietnam November 10, 2017.
Abe said he proposed to visit China at an appropriate time, which would then be followed by a Xi visit to Japan.
A North Korean soldier defected to South Korea through the Joint Security Area (JSA) in the demilitarized zone Monday, the Joint Chiefs of Staff said.
Japanese Prime Minister Shinzo Abe and Xi have also agreed to deepen cooperation between the two countries on North Korea, Abe said on Saturday after meeting Xi.
Kang Kyung-wha is to visit Beijing "as early as next week" to discuss detailed preparations for the third summit between South Korean President Moon Jae-in and his Chinese counterpart Xi Jinping scheduled for next month, according to the source.
The sabre-rattling has complicated China's relations with South Korea.
Xi urged South Korea to take a "responsible attitude on THAAD that stands the test of history", adding that it would be "new beginnings and a good start". A Cheong Wa Dae official said, "President Moon said that THAAD is not aimed at China". "Xi said that South Korea-China relations are at a critical point and that the two countries must respect their key interests and their grave concerns, safeguard reciprocal trust in political affairs and strengthen communication and cooperation", China's Foreign Ministry reported.
The Chinese leader also encouraged South Korea to resume dialogue with North Korea and re-engage with them for reconciliation and de-nuclearisation.
"Better not to be too optimistic".
Also on Saturday, the US and South Korea launched a joint naval drill in a show of strength against the North's leader Kim Jong-un. The four-day exercise in the western Pacific involves three US aircraft carriers - USS Ronald Reagan, USS Nimitz and USS Theodore Roosevelt - and seven South Korean warships including three destroyers.