Atalay said the mandate was not a war-cry but rather a "deterrent" against the Syrian army.
"This mandate is not a war mandate but it is in our hands to be used when need be in order to protect Turkey's own interests according to potential developments in the future," said Atalay in remarks televised by NTV news channel
The deputy premier also said Syria assured that "such an incident would not be repeated."
The motion was approved by 320 MPs in the 550-seat Turkish parliament in an emergency session.
The shelling on Wednesday killed five Turks, including a mother and her three children in the border town of Akcakale in the southeast.