The civil protection agency said the city, as well as other parts of Liguria and northern Tuscany, will remain on high alert until midnight on Wednesday.
The floods last month caused millions of euros in damage, with Italy's Prime Minister Matteo Renzi later saying that €2 billion would be given to the city to build safety measures.
Antonio Campanella, a 57-year-old nurse, drowned after the river Bisagno burst its banks. His body was found in an underpass close Genoa Brignole train station.
Three women died a few days later when torrential rain swept through Tuscany.
The floods are the worst to hit Genoa since 2011, when six people, including two children, were killed.
Persistent rain is also forecast to hit the rest of the country over the next couple of days, with the only regions spared being Veneto and parts of Romagna. Snow is also expected in the Alps.