NEW DELHI, Aug. 27—The Indian Government said today that it was continuing to maintain normal diplomatic relations with neighboring Bangladesh.

The official announcement amounted to diplomatic recognition of the Government of President Khondakar Mushtaque Ahmed, who took office after the overthrow and assassination of Sheik Mujibur Rahman on Aug. 15.

India, which had very friendly relations with Sheik Mujib's Government, had not formally recognized the government of his successor, although there have been recent diplomatic contacts between the two countries. Recalling these contacts today, the Government spokesman said: “It would be clear from all this that we continue to recognize Bangladesh.”

Prime Minister Indira Gandhi, who deplored the military coup d'état at the time, said in an interview made public today: “It is our sincere hope that the present leaders of Bangladesh will continue to work for the objective of goodwill, and cooperation on the subcontinent.”