Speaking in the capital Nairobi, he said he had talked with Kenyan President Uhuru Kenyatta "at length" about how the UN and Kenyan government can work together in countering "heinous" attacks.
"(The) UN is determined to work together with the Kenyan government in helping enhancing the capacities of the Kenyan government and many African countries who are suffering from this international terrorism," he said, although he did not give further details of what form any assistance might take.
Kenya has been the scene of a series of attacks attributed to the Somali Al-Qaeda-linked group Shebab and their supporters since Kenya sent troops over the border to help fight the group in 2011.
The Shebab claimed responsibility for the assault on the Westgate shopping centre that killed at least 67 people in the Kenyan capital in September last year as well as for two nighttime attacks on the Kenyan coast in the middle of June that claimed around 60 lives.
During their interview, the president and secretary-general also discussed Somalia, the crisis-hit South Sudan, and the Great Lakes region, where tensions remain high between the Democratic Republic of Congo and Rwanda.
Ban arrived in the Kenyan capital at the close of a UN Environment summit. As part of the trip he also visited the Nairobi National Park where the UN is working to fight the traffic in fauna and flora, where he adopted a six-month old lion cub.