His statement came on Friday evening.
However, Dang later claimed that his statement was in the context of seeing the CAA and the National Register of Citizens (NRC) "separately" and "not defined together", adding that he had not spoken in favour of the CAA.
Even though the Centre has notified the Act on Saturday, Chief Minister Kamal Nath had said the state government would not enforce it.
"If we see CAA and NRC separately, there is no harm if unhappy people living in Pakistan, Bangladesh and Afghanistan are getting facilities here. But we also have to think if people living in India have to furnish documents (under NRC)," Dang said.
Queried on his support for CAA, the Congress MLA said, "It would be wrong to say I have supported CAA. I believe CAA and NRC have to seen separately. It would be wrong if these are defined together."
Dang opposed the NRC and said it was causing confusion among people, adding that as far as citizenship was concerned, even people living in this country since ages do not have documents to prove it.
Dang had earlier resented being left out of the ministry and therefore questions were raised about his loyalty to the party.
A few days ago, BSP MLA Rambai had also announced her support to the CAA before retracting after party Supremo Mayawati suspended her.
Last month, a senior member of the Congress, Laxman Singh, who is the brother of former Chief Minister Digvijaya Singh, had also suggested that the Congress should accept the citizenship law and move on.
( With inputs from IANS )