The weather office advised maritime ports of Chattogram, Cox's Bazar, Mongla and Payra to keep hoisted local cautionary signal No 3 on Tuesday.
It also asked fishing trawlers and boats to remain close to the coast until further notice, according to the Met office.
Due to strong monsoon and steep pressure gradient over the North Bay, squally weather may hit the maritime ports, North Bay and adjoining coastal areas of Bangladesh, said a met office bulletin.
The met office said that light to moderate rain or thundershowers accompanied by temporary gusty wind is likely to occur at most places over Rangpur, Khulna, Barishal, Chattogram and Sylhet divisions, at many places over Dhaka, Mymensingh and Rajshahi divisions with moderately heavy to heavy falls at some places over the country.
Day and night temperature may remain nearly unchanged all over the country.
The axis of monsoon trough runs through Rajasthan, Haryana, Uttar Pradesh, Bihar, Gangetic West Bengal to Assam across central part of Bangladesh. Monsoon is fairly active over Bangladesh and strong over North Bay.