The incidents took place in two neighbourhoods, known as No. 1 Jhil and Bijoy Nagar, on early Saturday, according to Akbar Shah Police Station chief Wali Uddin Akbar.
The dead have been identified as Shahinur Akter, 26, Mainur Akter, 24, Liton, 24, and Emon,14.
A landslide buried a house by the hill at No. 1 Jhil. The fire service retrieved four people from under the rubble.
Shahinur and her sister Mainur were declared dead by a doctor in a local hospital. Their parents, Fazal Haque and Moshara Begum, are still undergoing treatment.
Liton and Emon died in a similar landslide in Bijoy Nagar.