Khosty denied the assault accusations, saying he had divorced Elaha after what he called a “consensual marriage”.
“In February, Saeed Khosty, who was the spokesman for the interior ministry, forcefully married me inside the intelligence department,” she said, without specifying how the two had met.
“I was beaten. I was raped there. I didn’t know what to do,” she said.
She said she was asked to apologise to Khosty, and when she refused she was “beaten”.
It was not known where Elaha had posted the video from, or where she was now.
On Twitter, Khosty denied the accusations.
“She had some issues regarding beliefs and faith. I tried to correct her through discussions and advice, but it did not work,” the Taliban official said.
“I have not beaten her, but exercising my Islamic rights I divorced her. I regret my marriage to her, which I had entered into hastily.”
He said Elaha was free to file a case against him if she wished.
“I apologise to the mujahideen of the Islamic Emirate and Afghan nation. May God forgive me,” Khosty said.
“If I’m proved guilty, the court can punish me. If she does not believe in the courts of the Islamic Emirate, then I’m ready to go to any court that she wants.”
After Elaha’s video emerged, the hashtag #justiceforElaha went viral on social media.
Khosty received support online from some Taliban members.
“Unless a court convicts him, he is not a criminal for me,” tweeted former Kabul police spokesman General Mobeen Khan.
Last year, Taliban Supreme Leader Hibatullah Akhundzada issued a decree ordering authorities to take strict action against those who “force women to marry by coercion or pressure”.
Since returning to power last year, the Taliban have enforced a series of strict rules on the conduct of women, especially in relation to public life.
The hardline Islamists have shut girls’ secondary schools in most provinces and barred women from many government jobs.
They have also ordered women to fully cover up in public, ideally with an all-encompassing burqa.