The council and key partners have been closely monitoring conditions following Friday's heavy rainfall.
Water levels at the River Esk in Musselburgh are believed to have peaked on Friday afternoon.
Council teams, who have been on stand-by to respond to any challenges which emerge, put sandbags in place at points along the riverbank as a precautionary measure ahead of high tide on Friday evening.
This followed the issuing of a flood warning by the Scottish Environment Protection Agency for the Esk at Musselburgh.
While it is hoped weather conditions will be generally improved over the coming days, there is likely to be some further rainfall on Sunday and early next week.
Although river levels have dropped since Friday morning, sandbags will remain in place as a precaution into next week.
Water levels at other watercourses, including the River Tyne, also continue to be monitored.
The council and key partners such as Police Scotland and the Scottish Environment Protection Agency will continue to monitor the situation.