Ghanaian media reported that a plane left Ghana for Brazil with the bonus money in cash -- between $1.7 and $2.3 million -- as players didn't trust that they would be paid by electronic transfer.
"President Mahama waded into the matter after agitation from the Black Stars players over their appearance fees for the World Cup which has not been paid since the start of the competition," the GFA said. The federation said the president's intervention had "brought some assurance to the Black Stars."
Reports say Ghana's squad was promised between $75,000 and $100,000 each for playing at the World Cup. The GFA didn't give a figure.
"The players insisted that they will want physical cash," Deputy Sports Minister Joseph Yammin said in comments broadcast by Accra-based Citi FM, according to Bloomberg. "Government had to mobilize the money and a chartered flight to Brazil. The money is in excess of $3 million."
There was clearly unrest in the camp, prompting President Mahama to speak to captain Asamoah Gyan and other senior players on the telephone. The squad has now arrived in Brasilia for the Portugal game after threatening a boycott.
Like other African countries playing at the World Cup, Ghana's government is financing the player bonuses. The money will later be reimbursed by some of the prize money -- of at least $8 million -- that FIFA guarantees each country, even if it is knocked out in the group stage. That won't be paid to Ghana until after the tournament, the GFA said. FIFA also gives each of the 32 teams competing $1.5 million beforehand to help with preparation costs.
Before the tournament, Cameroon's squad refused to board a plane to Brazil from Yaounde until their demands for improved bonuses were met. There have also been rumblings of discontent over pay in the Nigeria and Ivory Coast camps at the World Cup.
Ghana was Africa's only team to qualify for the second round at the last World Cup and reached the quarterfinals. In Brazil, it needs to win against Portugal on Thursday and hope Germany beats the United States heavily in the other group game to advance.
"We wish to assure the general public (that) following President Mahama's intervention the Black Stars are in high spirits ahead of Thursday's match," the GFA said.
Information from The Associated Press was used in this report.
Ghana's 'delicate' World Cup bonus situation
The Last Call crew discuss the situation in which Ghana's players have been unhappy about not receiving bonus payments.
No distractions for Ghana
Ghana train at Estadio Rei Pele in preparation for their game against Portugal on Thursday. Coach James Appiah is keeping his squad focused on the job in hand, and blocking out the off field distractions.