Brunson, an Evangelical pastor residing in the coastal province of Izmir, is standing trial in Turkey over terrorism charges.
Turkey has been hit by a currency crisis fuelled by a heated row with the United States.
The Turkish Lira has lost almost 40 percent of its value against the U.S. dollar since the start of the year.
Turkey has been rocked in recent days by a sharp decline in the value of its lira after US President Donald Trump tweeted last Friday that Washington was doubling aluminum and steel tariffs for Ankara.
In recent weeks, the USA has sanctioned a pair of Turkish cabinet members, and dramatically increased tariffs against the nation, fueling anger among Turkish leaders and creating economic uncertainty across the region.
Turkey retaliated with tariffs on some U.S. imports and said it would boycott USA electronic goods.
Also worrying investors has been President Recep Tayyip Erdogan's refusal to allow the central bank to raise interest rates to support the currency, as experts say it should.
Mr Erdogan is angry that the USA has not taken more action against the Gulenist movement and what he said was a failure "to unequivocally condemn" the 2016 coup attempt.
Trump later said in a tweet the United States "will pay nothing" for Brunson's release, "but we are cutting back on Turkey!"
Last week, Trump announced on Twitter that he had green-lit a doubling of steel and aluminum tariffs on Turkey, and warned that U.S. relations with Turkey "are not good at this time!"
In what could be interpreted as a sign of further tensions, the Turkish president said at a meeting with ambassadors on August 13, that Turkey is ready for war, as reported by the Turkish news service Ahval.
"We have responded to the measures the United States has taken, and will continue to do so based on our worldwide trade law rights and in accordance to World Trade Organization rules", said the minister, Ruhsar Pekcan.
Whatever action the United States takes looks likely to cause more pain for Turkish assets.
At 1827 GMT the currency TRYTOM=D3 stood at 6.0350 to the dollar, 4 percent weaker after tumbling as much as 7 percent earlier.
"Turkey will emerge stronger from these [currency] fluctuations", he said on Thursday as he addressed foreign investors and economists from the US, Europe and Asia via a conference call in a bid to soothe the markets.
Standard & Poor's is scheduled to release a review of Turkey's sovereign credit rating later on Friday.
Qatar pledged $15 billion of investment in Turkey on Wednesday that a government source in Ankara said would be channeled into its banks and financial markets.