Earlier Friday, Japan and Russia agreed to continue discussing a territorial dispute that has kept the nations from signing a peace treaty.
"We need to act constructively. We should not be emotional, and avoid provocative remarks," Lavrov said in Friday's news conference.
The diplomats also agreed to hold vice-ministerial talks in late January or February, ahead of Kishida's planned visit to Russia in the spring.
Lavrov did not mention an attack on Russian missiles in Latakia in Syria. Kishida said he and Lavrov planned to discuss Syria, Iran, Afghanistan and other international issues at Friday's working dinner, which was closed to the media.
Japan is seeking to broaden its defense ties, in addition to its key security alliance with the United States, in response to China's growing military presence and threats from North Korea.
Russia has been expanding its trade ties in Asia and President Vladimir Putin has actively sought closer relations with Japan, partly as a counter to China's rising military power.
It's unclear how much progress is being made toward a resolution of a dispute over four islands that were seized by Soviet forces at the end of World War II. The dispute has kept the two nations from signing a peace treaty formally ending their World War II hostilities.
Japan and Russia have also stepped up cooperation in developing energy resources, especially liquefied natural gas. Kishida said trade between the two countries totaled a record $33 billion last year, and that further growth is expected this year.
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Associated Press writer Emily Wang contributed to this report.