The high-rank men took the opportunity to discuss an array of geopolitical issues during the meeting, which included dinner.
Akiba conveyed Japan's position on Taiwan to Yang and stressed the importance of peace and stability in the Taiwan Strait, the National Security Secretariat official said.
Their meeting was held a fortnight after a visit to Taiwan by United States House Speaker Nancy Pelosi sparked a furious reaction from the Chinese government, which launched its largest military drills around the self-ruled island, which it considers its own territory.
Japan's security adviser said that Prime Minister Fumio Kishida condemned and protested Beijing's recent show of military might.
The pair exchanged views on international and regional issues of common concern, but did not give details.
Akiba and Yang also talked about a longstanding dispute over disputed islets in the East China Sea - known as the Senkaku by Tokyo and the Diaoyu by Beijing - the official said.
In July, Japan lodged a protest against China over a Chinese naval vessel sailing near the islands.
Akiba reiterated Japan's position over the islets as well as China's growing maritime assertiveness, the official said.