A Turkish court Friday rejected the appeal for release filed by American pastor Andrew Brunson, who is charged with links to terrorism. Turkish officials say the case is a matter for the courts.
"We have put sanctions on several of their cabinet members", said Mnuchin. "He's not a spy".
The US has threatened to impose more economic sanctions on Turkey if it does not free a detained American pastor.
Analysts also said the political cost of the investment remained to be seen, given that Qatar is also a U.S. ally and dependent on Washington for both military and political protection. We are not going to take it sitting down.
After hitting a record low of 7.24 this week, the lira has benefited from central bank steps to underpin a currency hit by concerns at President Tayyip Erdogan's influence over monetary policy and a bitter dispute with Washington.
Only one day after Qatar pledged the investment, the lira strengthened some 4 percent against the greenback to around 5.75 per dollar.
The US insists the pastor, a long-time Turkish resident, is "a victim of unfair and unjust detention".
Speaking as he left the White House on Friday, Trump told reporters on the South Lawn: "They have a wonderful Christian pastor".
Albayrak's ministry said they had discussed US sanctions against Turkey and agreed to act together in responding to such moves and to boost cooperation between their countries.
"It nearly seems as if Trump's words were an invitation for there to be even more of an entrenchment of this dispute", said Al Jazeera's Sonia Gallego, reporting from Turkey's largest city of Istanbul. "Our relations with Turkey are not good at this time!"
He says the US will pay nothing for his return, because he is innocent and indicated the pressure on Turkey will continue. Mr Brunson denies any involvement.
In addition to its decision to ramp up tariffs on imports of Turkish steel and aluminium, the Trump administration imposed sanctions on two top officials in Erdogan's cabinet earlier this month as part of its efforts to pressure Ankara into freeing Brunson. Turkey's banking watchdog on Wednesday also moved to crack down on shorting of the lira.
Trump, who has doubled steel and aluminum tariffs on Turkey, said the steel tariffs had kicked in and the aluminum tariffs would take effect soon.