The Turkish Finance Ministry said earlier that both ministers discussed US sanctions imposed on Turkey, which have worsened a row between the North Atlantic Treaty Organisation allies and sent the lira currency to a record low against the dollar.
The lira hit a record low of 7.24 against the USA dollar over concerns about President Tayyip Erdogan's grip on monetary policy and an ongoing row with the United States.
In a tweet on Thursday, Trump urged Brunson to serve as a "great patriot hostage" while he is jailed and criticized Turkey for "holding our wonderful Christian Pastor".
Trump, who doubled steel and aluminum tariffs on Turkey, said the steel tariffs have kicked in the aluminum tariffs will take effect soon.
The United States on Wednesday imposed sanctions on a Russian port service agency and Chinese firms for aiding North Korean ships and selling alcohol and tobacco to Pyongyang in breach of USA sanctions aimed at pressuring North Korea to end its nuclear programs.
The lira lost strength after Mnuchin's remarks.
Last Friday, U.S. President Donald Trump said he had authorised higher tariffs on aluminium and steel imports from Turkey. The US has already increased its sanctions against Turkey.
Trump's Russian Federation denial 'hogwash', blasts Brennan
Brennan has been a familiar face on television news shows where he has made scathing attacks on the president. She also questioned Brennan's "objectivity and credibility".
On Wednesday, the United States dismisses any move to remove steel tariffs which caused currency rout in the Turkey even in the circumstance if Ankara frees a USA pastor.
Turkish President Erdogan has slapped new tariffs on American products like cars, alcohol and coal. Trump added the pastor is a "very innocent man" and "we got somebody out for him - he needed help getting somebody out of some place".
The Turkish currency was trading at 5.85 at 1740 GMT, more than 1 percent stronger on the day. Ankara also wanted Washington to hand over Turkish cleric Fethullah Gulen, who lives in Pennsylvania and who Turkey suspects of plotting the coup against Erdogan.
The Eurasian country's president, Recep Tayyip Erdogan, announced on Tuesday that he would be calling for a boycott of all American electronics sold to the country's residents.
Analysts say Turkey is also likely to seek a more dynamic economic relationship with China and Russian Federation, with whom ties have warmed considerably in recent years.
"Turkey isn't in favor of an economic war", Ibrahim Kalin said Wednesday, "but staying silent when attacked is out of question".
The currency gained some support from the announcement late yesterday of a Qatari pledge to invest $15 billion in Turkey.