In the video, the security expert said some words to his side lover while on a National duty outside the country.
The side chic, who is believed to have recorded the video, does not show her face but kept instructing the minister to show his face and what he was wearing.
The leaked video since surfacing on the internet has triggered various reactions from Ghanaians with some calling on him to resign.
Security expert Adam Bonaa urged Kan Dapaah to resign.
He said the minister should have known better and must have exercised better judgment.
In an interview on Accra-based Starr FM, he said It's very very disturbing. It could happen to anyone. But I believe that at certain positions we ought to be circumspect. The national security minister should have known better.
"As far as I'm concerned it is despicable. If he wasn't a national security minister, it won’t have been much but because he is a National security minister this is unacceptable. If I were him, it would have been prudent to resign by now. It’s taking too long, we haven’t heard anything."
The Executive Director of the Centre for Human Security and Peace Building, Adib Saani, called for the head of Kan Dapaah.
He said "for him to get embroiled in such a reckless act and exercising such poor judgment speaks a lot about how messy a Kan Dapaah-led National Security Ministry is. If a National Security Minister can easily be set up by a lady and exposed in such a fashion, the probability of him getting compromised is certainly high."
On the part of the controversial musician, Kwame Asare Obeng aka A-Plus has called on the National Security Minister to resign for his amorous conversation with his side-chick while on a national assignment.
A Plus also called on Ghanaians to be lenient and forgive the respected minister describing his behaviour in the leaked video call as unfortunate.
As for resign, no doubt, he must resign. I feel sorry for him. It is unfortunate that this has happened to a respected democrat like Albert Kan Dapaah. (The thing pain me rough.)
This is not something to rejoice over. We must rather learn from it. I wish he would be the honorable man we know him to be by accept responsibility, apologizing to his family, loved ones and Ghana.
And please, please, I beg you, let's all forgive him. When the heart pumps blood into that "langalanga" between our legs, the mind in most cases switches of the part that is meant for caution. Please kindly be lenient towards him.
Don't discuss...." he wrote on his Facebook page.