The work, which began Aug 31, has so far done about 200 metres of the 22-kilometre Klong Lat Phrao.
Col Noppadol Pinthong, commander of the mobile unit of Armed Forces Development Command said that the unit took over the work from the Science and Technology Ministry.
Before the dredging operation started, officers visited residents along the canal and explained about the operation.
Col Noppadol said a large number of houses have encroached upon the canal, so the dredging operation has been done slowly. He asserted, however, that dredging all four canals will be completed at the end of this month.
The Bangkok Metropolitan Administration has assigned municipal workers to help with the military operation.
The problem of construction trespassing into city canals must be dealt by high level government officials. The military has a duty to create understanding with local residents and to prevent any impact on them, he said.