The officials told Mr Singh that Mr Dwivedi, a joint secretary, has been "wrongly punished" for the alleged lapses of his juniors, who reportedly facilitated the renewed licence for the Islamic Research Foundation.
Sources say the officers, mostly from the IAS or Indian Administrative Service, told Mr Singh that punishing an honest officer like Mr Dwivedi sends the "wrong signal" and is "demoralising" for others.
The home minister assured the officials that he would look into the matter, the sources said.
Mr Dwivedi has also separately met Mr Singh to plead his case.
Mumbai-based Naik, 50, is being investigated for his incendiary speeches. He has been accused by the Bangladesh government of making speeches that could have incited some of the terrorists who attacked a Dhaka cafe in July, killing 20 people.
It is unusual for senior bureaucrats to come out in protest against their colleague being punished. On Saturday, four officials had also met Union Home Secretary Rajiv Mehrishi.
"It is demoralising for honest officers, I feel injustice has been done to Mr Dwivedi. We have conveyed our feeling," Joint Secretary Kumar Alok of the home ministry had said after meeting the home secretary.
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