"We have more that we are planning to do if they don't release him quickly", Mnuchin said.
Mnuchin made the statement Thursday during a Cabinet meeting with the president attended by journalists.
"We've seen no evidence that Pastor Brunson has done anything wrong and we believe he is a victim of unfair and unjust detention by the government of Turkey", White House Press Secretary Sarah Sanders said at the time.
Ankara accuses Mr Brunson - who operates a tiny evangelical church in Izmir - of having links to the outlawed Kurdistan Workers Party and the Gulenist movement, which Turkey blames for a failed coup two years ago.
In a conference call with thousands of investors and economists, Albayrak - who is President Tayyip Erdogan's son-in-law - said Turkey fully understood and recognized all its domestic challenges but was dealing with what he described as a market anomaly.
The Turkish lira has strengthened more than 3% today, ahead of a presentation by Finance Minister Berat Albayrak to investors, shrugging off USA comments ruling out the removal of steel tariffs on Turkey even if it frees a United States pastor.
"Pastor Andrew Brunson is an innocent man held in Turkey & justice demands that he be released. Not fair, not right".
Washington has already placed a series of sanctions against Turkey, including last week's announcement of a doubling of tariffs on metal imports into the USA from Turkey.
Former White House aide says she recorded sacking to ‘protect herself’
Manigault Newman questioned who holds power in the White House . "I don't want to negotiate", Manigault Newman replied. I just saw in the news that you're thinking about leaving. "So I protected myself and now I am glad I did".
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".
Turkish Foreign Minister Mevlut Cavusoglu struck a somewhat conciliatory note, saying Turkey was ready to discuss its issues with the United States as long as there are no threats.
A day earlier, he said the United States was seeking to stab Turkey "in the back" by sending the lira into a tailspin.
The lira gained some support from the announcement late on Wednesday of a Qatari pledge to invest $15 billion in Turkey.
The two North Atlantic Treaty Organisation allies have traded tit-for-tat sanctions over the pastor's house arrest.
There was also optimism about better relations with the European Union after a Turkish court released two Greek soldiers pending trial.
Turkey's finance minister Berat Albayrak has insisted that the country will come out out the currency crises stronger.