"This is absolutely wrong. No politician should pass comments on the Army chief," Gandhi said.
Earlier, BJP on Monday attacked the Congress and demanded an apology from its chief Sonia Gandhi over Dikshit's remarks.
The Congress had shown a "consistent pattern" in undermining democratic institutions and it was shocking that its leader had now targeted the Army, Union minister Nirmala Sitharaman said at a press conference.
Dikshit had tendered an apology, saying he had reservations about Army Chief Bipin Rawat's comments but should have chosen appropriate words.
"There is no sense of apology in his tweets. No less than Congress president Sonia Gandhi should come out and apologise," Sitharaman said.
Calling Dikshit, a former Lok Sabha MP, an eminent leader and well-known face, she said the Congress should disown him for trying to shame and demoralise the Army.
Dikshit had stoked a controversy with his description of Army chief General Rawat as a "sadak ka gunda", leading to outrage.
Speaking to ANI, Dikshit had said, "It feels our army chief speaks like a roadside thug. While this is expected from Pakistan who are like the mafia, why does our own chief make such pronouncements?"
Dikhsit's remark came in the backdrop of General Rawat's recent statement, where he said that the Indian Army is well prepared to face external and internal threats of the country.
"Indian Army is fully ready for a two-and-a-half front war", General Rawat had said.
The Congress party had already sidelined itself from Dikshit's controversial statement, saying that the party does not support use of such language at all.
"I don't know why he used such language. We have discussed this issue with him, but the party doesn't support this for sure," Congress leader Meem Afzal told ANI.
(With inputs from agencies)