"Praying for the safety of the hostages in Bangladesh," Clinton tweeted.
"To the terrorists: We will never succumb to fear and hate," she said.
As Secretary of State, Clinton had visited Bangladesh in May 2012 and had a signed memorandum of understanding with her counterpart to create the US-Bangladesh Partnership Dialogue.
The fifth edition of the annual dialogue was held in Washington DC last week.
Suspected Islamic State terrorists last night stormed a restaurant in Dhaka's Gulshan diplomatic area and took hostage at least 20 people including foreigners, triggering a fierce gun battle with Bangladesh security forces in which two policemen were killed and 30 injured.