The lira stood at 6.0050 against the dollar at 1351 GMT, having gained from Monday's close of 6.0650.
Earlier it firmed to as much as 5.9940, its strongest level in more than a week.
The currency has been battered this year by disagreement between Ankara and Washington over Turkey's purchase of the S-400s, which the US says could compromise its F-35 fighter jets.
Broadcaster Haberturk quoted Akar as saying in an interview on Monday that the delivery of the S-400 may not happen in June, when Turkey previously said the missiles were due to arrive.
However, he added the agreement was a done deal.
"They may not make it by June but they will come in the months ahead.
The process has begun," he was quoted as saying.
A forex trader, speaking on condition of anonymity, said the lira received a bid versus other emerging markets.
"An optimism arose regarding the relations between Turkey and the United States.
Of course, the view isn't that all the problems are left behind," the trader said.
Optimism also emerged earlier this month after reports that the United States had asked Turkey to delay delivery of the S-400s, even while a senior Turkish official said Ankara's position had not changed.
The main share index was up 2.32pc, while the banking index rose 2.37pc.