Earlier this month, Washington imposed tough economic sanctions on Turkey's justice minister and interior minister for not releasing Andrew Brunson, an evangelical Presbyterian pastor from North Carolina.
He has denied the charges, and his case has been taken up by US President Donald Trump, who counts evangelical Christians among his core supporters.
The embattled currency, which has fallen by 40% this year amid a lack of interest rate hikes to control inflation, fell to around 5.86 to the dollar - continuing its recovery from a record low of 7.23 on Sunday.
"We have more that we are planning to do if they don't release him [Brunson] quickly", Mnuchin said, BBC reported. His transfer to house arrest came after Trump asked Israeli Prime Minister Benjamin Netanyahu to assist in Brunson's release, Israeli and U.S. officials told CNN at the time.
"They have not proven to be a good friend", Trump said of Turkey during the Cabinet meeting. "We are not going to take it sitting down, they can't take our people so we will see happens".
Brunson has lived in Istanbul for more than 20 years and held under house arrest for almost two on espionage and terror-related charges.
Last week, the United States doubled its tariffs on metal imports from Turkey.
Turkish lira weakens to 5.86, US warns of more sanctions
A Trump tweet last week announcing a doubling of aluminum and steel tariffs for Turkey triggered the rout in the currency markets. The lira gained some support from the announcement late on Wednesday of a Qatari pledge to invest $15 billion in Turkey.
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.
Many countries have been the target of similar U.S. trade measures, Albayrak said, and Turkey would navigate this period with other parties such as Germany, Russia and China. He criticized Turkey for "holding our wonderful Christian Pastor". Brunson's next hearing is scheduled for October 12.
In fact, Arriaga says all Americans can apply pressure by hitting Turkey where it hurts the most - in the pocketbook by avoiding buying Turkish goods.
Turkey retaliated with some $533 million of tariffs on some United States imports - including cars, tobacco and alcoholic drinks - and said it would boycott U.S. electronic goods.
"We will pay nothing for the release of an innocent man, but we are cutting back on Turkey".
Turkey's finance chief tried to reassure thousands of worldwide investors on a conference call Thursday, in which he pledged to fix the economic troubles.
Finance Minister Berat Albayrak, the son-in-law of President Recep Tayyip Erdogan, addressed hundreds of foreign investors from the United States, Europe and Asia via a conference call in a bid to soothe the markets. If convicted, he faces up to 35 years in jail.