"We have put sanctions on several of their cabinet members", said Mnuchin.
On Thursday, Trump tweeted that the USA would "pay nothing" for the release of Brunson, but would punish Ankara if he is not released.
Brunson, a 50-year-old evangelical pastor, faces 35 years in prison on charges of espionage and terror-related charges.
While Erdogan has said Turkey would respond to the sanctions by boycotting US goods, Aljazerra reported Foreign Minister Mevlut Cavusoglu is sending a more positive message but cautioned about the Trump administration on its tone in future negotiations.
Speaking as he left the White House on Friday, Trump told reporters on the South Lawn: "They have a wonderful Christian pastor".
"President Trump's imposition of tariffs on steel and aluminum is about protecting American national security", the spokesperson said.
Last week, the USA doubled its tariffs on metal imports from Turkey.
"We're going to continue to apply the pressure until you do", Brownback said.
Turkish president says the country will boycott United States electronics
The clergyman is at the center of heightened tensions between North Atlantic Treaty Organisation allies, Turkey and the U.S. Turkey's exports to the United States past year amounted to $8.7 billion, making it Turkey's fifth-largest export market.
Last week, Washington doubled steel and aluminium tariffs on Turkey over its continued detention of U.S. pastor Andrew Brunson.
The United States was the fourth-largest source of imports to Turkey past year, accounting for $12 billion of imports, according to International Monetary Fund statistics.
Turkey says the case is a matter for the courts.
In an article for the New York Times, published last Friday, the Turkish leader said Turkey "had rushed to America's help whenever necessary" in various times, from the Cold War to the more recent conflicts in Afghanistan, Iraq and Syria.
Turkey's finance chief tried to reassure thousands of global investors on a conference call Thursday, in which he pledged to fix the economic troubles.
The turmoil has raised fears of a looming economic crisis in Turkey and prompted alarm that foreign investors in the country, including Qatar, could be hit in the fallout.
Mr. Trump wrote in a tweet late Thursday: "We will pay nothing for the release of an innocent man, but we are cutting back on Turkey!"
The currency has lost almost 40 percent against the dollar this year, driven by worries over Erdogan's growing influence on the economy and his repeated calls for lower interest rates despite high inflation.