Gyan announced on Monday that he did not want to be part of coach Kwasi Appiah's side after learning of plans to change his leadership role in the team during the Africa Cup of Nations in Egypt in June.
"Upon consultation with my family and team, if the decision of the coach is to give captaincy of the tournament to another player while I am named in the team for the tournament, I wish to recuse myself from the tournament," Gyan said a statement. "I also wish to retire from the national team permanently."
Gyan, who plies his trade for the Turkish top flight side Kayserispor, has, since his debut in 2003, amassed 106 caps for Ghana during a club career that has taken him from Ghana to Europe, China and the Middle East.
He is the country's leading marksman with 51 strikes in games spanning three World Cups and half a dozen Cup of Nations finals.
Aware of the national significance of Gyan's departure, Akufo-Addo telephoned the player and urged him to be part of Appiah's plans.
"A presidential request is one that cannot be disregarded," said Gyan in a statement on Wednesday. "I have taken the request of His Excellency Nana Addo Dankwa Akufo-Addo in good faith and will make myself available for selection.
"My desire to help Ghana end the over three-decade long wait to annex the trophy still burns strong, and I remain committed to serving this great nation and the people of Ghana."
Ghana won the fourth of their Cup of Nations crowns in 1982. They will begin their quest for a fifth title in Group F with defending champions Cameroon, Benin and Guinea-Bissau.