KABUL, Afghanistan — A political rival of Vice President Abdul Rashid Dostum of Afghanistan said on Tuesday that he had been tortured and raped with an assault rifle after being abducted by General Dostum last month.

In an interview with The New York Times, the political rival, Ahmad Ishchi, said he was badly abused by the general, who was the acting president at the time because President Ashraf Ghani was out of the country, and by the general’s men.

“I can kill you right now, and no one will ask,” Mr. Ishchi said General Dostum told him. He claimed the vice president stepped on his throat and pressed down after he had already been beaten and bloodied.

General Dostum’s office, in a statement, called the accusation a conspiracy to defame the vice president. The statement said Mr. Ishchi had not been abducted, but rather had been arrested by security forces on charges of supporting the opposition, for which he remains under investigation.