The 57-year-old, who is seeking a second term of office in November, has been accused of receiving a four-wheel-drive vehicle from a contractor in Burkina Faso bidding for a lucrative construction contract.
The main opposition New Patriotic Party and others allege the gift was designed to influence the awarding of a road building contract and the construction of a wall at Ghana's mission in Ouagadougou.
But Mahama yesterday accused the NPP of politicking.
"I've been president in this country, if you believe I have indulged in corruption you have the constitutional means to do what you want to do," he said.
Ghana's government has confirmed it received the car but maintained it was a gift, denying claims it was a bribe or conflict of interest.
The vehicle has been added to the government car pool, it added.
Some minority members of parliament have threatened to initiate impeachment proceedings against Mahama, arguing the president had no right and no need to accept the vehicle in the first place.
Mahama, who leads the National Democratic Congress (NDC) party, faces a challenge for the presidency from the veteran NPP head Nana Akufo-Addo.
