Hasina and her Awam League returned to power by registering a landslide victory in the election.
She did not mention the name of the country.
"Many have their eyes on this place. There is no controversy here, no conflict. I won't let that happen. This is also one of my crimes [in their eyes]," she was quoted as saying by Daily Star.
Speaking on the proposal to build an airbase, Hasina said: "The offer came from a white man."
"It may appear that it is aimed at only one country, but it is not. I know where else they intend to go," she said.
She claimed their is also a plot to create a 'Christian state like East Timor' taking parts from Bangladesh and Myanmar.
She said, "Like East Timor ... they will carve out a Christian country taking parts of Bangladesh [Chattogram] and Myanmar with a base in the Bay of Bengal."