The Prince of Wales and his wife Camilla, Duchess of Cornwall, sent a letter to Prime Minister Sheikh Hasina expressing their sympathy, her Press Secretary Ihsanul Karim said.
"We understand how dreadfully difficult this must have been as your people prepared to celebrate what should have been a joyful Eid."
Severe cyclonic storm Amphan made landfall in Bangladesh near the Sundarbans on May 20, lashing the country's coastal districts with strong winds and heavy rains before turning into a land depression.
At least 23 people died, mostly as a result of fallen trees and collapsed houses, while nearly half of the country's electricity consumers were left without power in the aftermath of the storm.
"Our greatest possible sympathy and our special prayers are with the people of Bangladesh at such a desperately anxious time, as you battle against the effects of both the COVID-19 pandemic and this appallingly severe storm," Prince Charles wrote.