Biswal, the Assistant Secretary of State for South and Central Asian Affairs, would meet Foreign Minister Abul Hassan Mahmood Ali.
She would also meet with Home Minister Asaduzzaman Khan Kamal, officials told bdnews24.
Earlier, the State Department said Biswal will meet with government officials to discuss "issues of shared concern" and offer US assistance to the Bangladeshi government's efforts to counter terrorism and violent extremism.
Bangladesh has witnessed a spate of Islamist attacks in recent days.
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Twenty-two people, including 17 foreigners, were killed in the brutal late-night attack at the Holey Artisan Bakery in Gulshan area of the capital on July 1. During a joint operation police killed six of the attackers.
Seventeen foreigners, including an Indian and American of Bangladesh origin were among the victims.
Six days later, militants attacked police guarding the largest Eid gathering in Bangladesh and killed three more people.
Biswal will also travel to Sri Lanka where she will meet with senior government officials and political leaders to discuss bilateral economic cooperation as well as democratic governance and reconciliation.
Biswal, earlier, visited Dhaka in May following the killing of a US embassy staff, Xulhaz Mannan, who was a leading campaigner for LGBT rights.