Ousted Bangladeshi prime minister Sheikh Hasina on Tuesday asked supporters to make a public show of strength later this week, hours after a court ruled that a murder probe against her linked to last month's unrest could proceed.

Hasina, 76, fled by helicopter last week to neighbouring India, where she remains, as protesters flooded Dhaka's streets in a dramatic end to her iron-fisted 15-year rule.

More than 450 people were killed during the weeks of unrest leading up to her toppling, and members of her Awami League party have since gone to the ground.

Thursday marks the anniversary of the 1975 assassination of her father, independence hero Sheikh Mujibur Rahman, during a military coup - a date her government had declared a national holiday.

"I appeal to you to observe the National Day of Mourning on Aug 15 with due respect and solemnity," she said in a written statement given to journalists through her US-based son.

She asked supporters to "pray for the salvation of all souls by offering floral garlands and praying" at her childhood home in the capital Dhaka.

Tuesday's statement was Hasina's first public comment since her resignation.

She also demanded an investigation into killings and other criminal acts during the unrest that forced her out of office, with the culprits to be "identified and punished".

Police weaponry was the cause of most deaths during the protests, according to police and hospital figures previously gathered by AFP.