He also apparently tried to profit personally from a $5 million-a-year, five-year sponsorship deal with the GFA in what the expose said was a "clear breach" of ethics.
Before the last World Cup in Brazil in 2014, Nyantakyi was accused of signing a $170,000-deal for Ghana to play in a friendly organised by match fixers.
The Ghanaian government has made a decision to shut down the Ghanaian Football Association following allegations of corruption in the organisation that have surfaced in recent days.
"I wish to apologise to my family, work colleagues, friends, associates and the people of Ghana for the disappointment my indiscretion has caused them". Ministers and Deputy Ministers of State for indiscretion in associating them with the private conversations on the video.
"It stemmed out of the controversies generated by investigative report of Tiger Eye PI", he added.
Ghana president Nana Akufo-Addo has called for criminal investigations against Nyantakyi.
Somalia conflict: One US soldier killed, four wounded in firefight
The coalition force was conducting a "multi-day operation" to clear al-Shabaab, an Islamist militant group, from nearby villages. A US Special Forces Operational Detachment Alpha (ODA) came under attack today in the Bar-Sanguni area near Kismayo in Somalia.
"In the said report I committed a series of errors of indiscretion".
FIFA have given Nyantakyi a 90-day ban from all football related activities with immediate effect.
"I wish to clarify that at no time prior to or subsequent to any deliberations on the video did I consult, contact or inform any government official about discussions on the video".
Asiamah said the decision had been a hard one to take, and is aware that it is likely to trigger some sort of action from world football's governing body FIFA, who strictly forbid the interference of government in the national federations.
BBC African football analyst Nick Cavell says it seems unlikely that Ghana will be able to take part in Wednesday's vote for the next host of the 2026 World Cup.
Nyantakyi, who is also a member of the Fifa Council, the world football body's legislative organ, was filmed in a hotel room allegedly taking a $65,000 bribe from a supposed businessman seeking to sponsor the Ghanaian football league.
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