He produced what he called key evidence at a press conference Friday.
The Democrat leader meanwhile threatened to file a defamation lawsuit against ACM Sukumpol if he continued making draft dodging allegations.
The threat coincided with the Friday press conference held by the minister.
The Democrat leader said he has refrained from publicly discussing the issue because a defamation trial is currently under way.
Mr Abhisit has filed a defamation suit against red-shirt leader Jatuporn Prompan for accusing him of evading conscription by using falsified documents to get a teaching job at Chulachomklao Military Academy.
By teaching at the military school, Mr Abhisit was exempted from mandatory conscription. The Democrat leader said the defence minister's actions are all politically motivated.
"I can't figure out what else it could be. I've clarified the matter several times. Everything coincides with my case against Mr Jatuporn," he said.
At the press conference, ACM Sukumpol produced documents which he said back his claim that Mr Abhisit dodged military conscription by using falsified documents.
He said he has ordered the Judge Advocate General's Department to consider stripping Mr Abhisit of his sub lieutenant rank and recalling his salary.
ACM Sukumpol denied his moves were politically motivated, saying he has acted in line with the Office of the Ombudsman's order to conduct an inquiry into the matter.
The defence minister said the ministry's inquiry has found that one of the documents Mr Abhisit has is not an "official" paper.
It is a letter verifying that Mr Abhisit registered for the reserve list on Jan 1 1982.
He also insisted there were discrepancies between the genuine Sor Dor 9 conscription document and a replacement. Mr Abhisit claimed he lost the original and obtained a replacement.
The original document stated that Mr Abhisit registered for the reserve list on July 4, 1986 while the replacement showed he registered on April 8, 1988.
"I am not going after anyone. Some people said I wouldn't dare go public," ACM Sukumpol said.
He declined to speculate whether his statements would influence any judicial decision in the defamation case between Mr Abhisit and Mr Jatuporn.
The Criminal Court will rule on the case on Sept 27.
The date was set yesterday after Asst Prof Worapol Promigabutr, a lecturer at the Faculty of Sociology and Anthropology at Thammasat University, testified as the final defence witness.
Mr Jatuporn made the accusation during red-shirt rallies in 2010.