Biswal, the US Assistant Secretary of State for South and Central Asian Affairs had an exclusive meeting with Indian High Commissioner in Dhaka Harsh Vardhan Shringla and discussed the security situation in Bangladesh.
An Indian diplomat preferring anonymity said Biswal herself sought the meeting with Shringla.
Biswal also met with the envoys of UK, Canada and Australia over the security situation in Bangladesh.
The US point person for South Asia, stayed there for around 20 minutes amid police barricade surrounding the area.
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The radical Islamic State (IS) has reportedly claimed responsibility for the attack on the popular eatery, which is frequented by foreigners. The second terror attack targeted the country's biggest Eid gathering at Sholakia in northern Kishoreganj district.
Biswal is visiting Dhaka following the two high-profile attacks and has offered Washington's support to build Bangladesh's capabilities in countering terrorism.
Meanwhile, Bangladesh today responded cautiously to the US
proposal for providing security assistance to the country in combating Islamist militancy saying the government would assess areas of requirement for possible American support.
"The United States has offered us expert assistance to enhance our capability to control terrorism," home minister Khan said after Biswal called on him here.
He added "We will assess what help we need. Then we will let them (US) know".
She underscored the US' "broad-based" understanding with Bangladesh and added that her country's support is an "extension of long and deep partnership based on shared values of democracy, tolerance and inclusion".
The IS and al-Qaeda in Indian Peninsula have claimed responsibility for some of the other attacks on Hindu priests, Christians and secular activists in Bangladesh however, the government denies the presence of IS or al-Qaeda in the country.
Police last month launched a nationwide anti-militancy week-long crackdown to halt these deadly attacks.