Mr Dave, the minister of state (independent charge) for environment, forest and climate change, was rushed to AIIMS here after he complained of uneasiness.
The 60-year-old BJP leader was declared dead in AIIMS. "The government today announced with profound sorrow the death of Anil Madhav Dave.
"As a mark of respect to the departed dignitary, the Centre has decided that the national flag will fly half-mast today in Delhi and all state and Union Territories capitals on all the buildings where it is flown regularly and on the day of the funeral where the funeral takes place," an official statement said.
Environment was a subject close to the heart of Mr Dave, who was appointed environment minister only last year.
Earlier Prime Minister Narendra Modi condoled the death of Mr Dave and termed his demise as a "personal loss".