Lavrov passed greetings from Russian President Vladimir Putin to Kim, saying he wished him success in the "major undertakings that have been initiated on the Korean peninsula", the ministry said in a statement.
The U.N. has blacklisted the North Korean tanker.
The meeting is created to salvage the planned summit between President Donald Trump and North Korean leader Kim Jong Un scheduled for June 12. "It may accommodate 80 to 90 percent of the USA demands for closure of its nuclear test site, suspension of nuclear tests, disabling of nuclear facilities and ICBMs and extensive nuclear inspections", said Kim at an global symposium on the North's human rights in Seoul. The monitoring is part of efforts to maintain pressure on Pyongyang to denuclearize.
The report said that Japan is seeking to hold the talks on the sidelines of the ASEAN Regional Forum (ARF) set to open on August first in Singapore.
The demolition was published in state media last week, but the actions taken were initially met with skepticism, Daily NK reported Saturday. "Nothing has been decided, including whether or not the minister would attend the Asean related meetings", he told a regular press conference.
Japan has reported to the United Nations another suspected transfer of goods on the high seas from a foreign ship to a North Korean tanker.
The last ministerial-level talks between Tokyo and Pyongyang were in 2015, also on the sidelines of an Asean meeting. Sanders said Trump will host Japanese Prime Minister Shinzo Abe of Japan on June 7 to co-ordinate their thinking ahead of the summit.
But he has also said Japan will need to eventually hold direct talks with North Korea to resolve an emotional row over abductions of Japanese nationals by Pyongyang.
Pompeo talks with Kim Yong Chol - the most critical of three tracks of negotiations now taking place between the two governments in the US, in the heavily fortified Korean Demilitarized Zone, and in Singapore - are aimed at determining whether a meeting between Trump and Kim Jong Un, originally scheduled for June 12 but later cancelled by Trump, can be restored.
Since then, meetings to prepare for the talks have resumed.