"We remain in contact with Bangladeshi authorities and have offered any assistance necessary," White House Press Secretary Josh Earnest said.
The "heinous" attack resulted in the death of an American citizen, Bangladeshi law enforcement personnel and citizens of several other nations, Earnest said.
"This is a despicable act of terrorism, and the US stands with Bangladesh and the international community in our resolve to confront terrorism wherever it occurs," he said.
The US has not disclosed the name of the American killed in the attack. "Out of respect for the family, we have no further comment. At this time, we are not aware of any other US citizens among those held hostage," State Department said.
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The spokesman said the threat that "terrorist ideologies" pose to the world does not require physical presence in a country. He said the US is troubled by recent attacks on secular bloggers, activists and minorities in Bangladesh.
"These attacks are being carried out by those who seek to stifle those who disagree with them," the spokesperson said.
"Bangladesh has a proud tradition of being a pluralistic society that values diversity and welcomes the free exchange of ideas. These are the values that the violent extremists are ultimately attacking," the official said.
The US is working with members of civil society and the media to support their efforts to counter the violent, hateful ideologies and to reinforce the great majority of Bangladeshi society that values diversity, freedom to peacefully practice religion, freedom of expression, and rule of law, he said.
"We support the Global Community Engagement and Resilience Fund (GCERF), of which Bangladesh is a pilot country. This funding supports grassroots projects to strengthen communities' resilience to violent extremism," he said.
US is also working with Bangladeshi police on community policing projects, with madrassa students to increase the economic opportunities for vulnerable youth, and with community leaders on conflict mitigation, he added.