Menon, who arrived here yesterday on a three-day visit, met Dai at the Diaoyutai State Guesthouse and the two officials along with their delegations held talks on the border dispute as well on other issues.
He is also expected to meet some of China's new leaders elected during the last month's Congress of the ruling Communist Party of China to succeed the outgoing administration headed by President Hu Jintao.
The NSA is expected to call on Vice Premier Li Keqiang, the number two leader in the seven member new Standing Committee of the party, headed by General Secretary Xi Jinping, who succeeded Hu.
Li is tipped to succeed Premier Wen Jiabao when he steps down in March after which a new administration headed by Xi would assume power formally.
Menon and Dai are designated as Special Representatives for the talks to resolve the border dispute.
Their meeting was not formally notified as 16th round of border talks apparently due to Dai's impending retirement.
Successor to Dai, who in Chinese hierarchy is called the State Councillor, was expected to be announced soon.
Besides talks with Chinese leaders, Menon will also release the book of Chinese translation of the works of Prof P C Bagchi, regarded as India's most eminent scholar on Chinese culture. He would also deliver a talk on India-China relations at the Indian Embassy here on December 4.