Turkey's currency, which had recovered from record losses against the dollar earlier in the week, was down about 6 percent against the dollar on Friday, at 6.17.
The lira has lost almost 40 percent of its value against the dollar this year, sparking a sell-off in emerging market currencies and weighing on global stocks.
Turkey has sought to persuade the United States to spare Turkey's state-owned Halkbank from a threatened fine for allegedly helping Iran evade USA sanctions. "He's a very innocent man", Trump said.
Brunson has now found himself in the middle of a diplomatic spat between the two countries, with US President Donald Trump authorizing new tariffs on steel an aluminium last week to put pressure on Ankara.
Mr Trump said: "They want to hold our wonderful pastor".
The lira has staged a small recovery but that is threatened by a fresh tweet from US President Donald Trump.
A court refused to release Mr Brunson, and the the government in Ankara increased tariffs on imports from the U.S. of cars, alcoholic drinks and leaf tobacco - and the lira recovered slightly. He demanded Brunson's release, saying "they can't take our people".
USA and Turkey relations have been souring, after President Trump doubled tariffs on Turkish steel and aluminum in response to his continued imprisonment. "This is very easy to resolve", the administration official said.
Investors said Albayrak's conference call would test whether Turkey can persuade markets that its monetary policy is not hostage to political influence.
The lira lost strength after Mnuchin's remarks.
"But one could hardly say the same about Turkey's announced tariffs on American cars, alcohol, and tobacco".