Mr Trump posted the threat on Twitter as the relationship between the two countries collapses amid the row over the release of America pastor Andrew Brunson, who has been charged with terrorism offences in Turkey.
Mr Trump said on Twitter: “Turkey has taken advantage of the United States for many years.
“They are now holding our wonderful Christian Pastor, who I must now ask to represent our Country as a great patriot hostage.
“We will pay nothing for the release of an innocent man, but we are cutting back on Turkey!”
Mr Brunson has been in dtention in Turkey since 2016 and is accused of being involved in the coup, which happened in the same year, against President Tayyip Erdogan.
Additional US sanctions against Turkey could be imposed if Mr Brunson is not freed.
The lira has lost almost 40 per cent of its value against the dollar this year, as the feud between Mr Trump and President Erdogan continuies to deepen.
Turkey’s Finance Minister, Berat Albayrak, has insisted that the country will come out out the currency crisis stronger.
See below for live updates
Tensions between the US and Turkey are continuing to escalate
7.30pm update: Turkey and France act together in response to US sanctions against Ankara
Turkish Finance Minister Berat Albayrak and Bruno Le Maire, his French counterpart, spoke by phone on Friday and discussed US sanction steps against Turkey, agreeing to act together in response to such moves, Albayrak’s ministry said.
The two minister decided to work closely to further cooperation between Turkey and France and agreed to meet in Paris on August 27, the statement said.
6.30pm update: American pastor should have already been freed, says Trump
President Donald Trump has said that an American pastor who is currently imprisoned in Turkey should have been released “a long time ago”.
Mr Trump’s comments come after a court in Turkey’s western Izmir province rejected an appeal to release Andrew Brunson from house arrest.
Speaking at the White House, Mr Trump said: “They should have given him back a long time ago, and Turkey has in my opinion acted very, very badly.
“So, we haven’t seen the last of that. We are not going to take it sitting down. They can’t take our people.”
5.30pm update: Emerging market equities pushed lower by steepening Turkish lira
Another steep decline in the Turkish lira on Friday pushed emerging market equities lower and kept other world markets cautious, overshadowing hopes that an upcoming US-China meeting would relieve concerns over trade tariffs.
MSCI’s All-Country World index, which tracks shares in 47 countries, fell less than 0.1 per cent, leaving the index on track for its third straight weekly decline.
A Chinese delegation led by Vice Minister of Commerce, Wang Shouwen, will meet US representatives, China’s Ministry of Commerce said in a statement, with the Wall Street Journal reporting that talks will take place in Washington on August 21 and 22.
The world’s two largest economies are due to slap tariffs on billions of dollars of each other’s goods on August 23, in addition to levies that took effect on July 6.
4.30pm update: Trump: ‘We are not going to take it sitting down’
Speaking on the American pastor detained in Turkey, President Donald Trump has said “we are not going to take it sitting down”.
He added: “We haven’t seen the last of that.”
3.30pm update: Turkish lira loses close to 40 per cent of value against dollar
The Turkish lira has lost nearly 40 per cent of its value against the dollar this year, hit by Ankara’s worsening rift with Washington and investor alarm about President Tayyip Erdogan’s influence over monetary policy.
Mr Erdogan, a self-described “enemy of interest rates”, wants to lower borrowing costs despite high inflation.
The lira crisis has deepened concerns about the broader economy – particular Turkey’s dependence on energy imports and whether foreign-currency debt levels pose a risk to the banking sector.
The Turkish lira has lost nearly 40 per cent of its value against the dollar this year
2.30pm update: US stock index futures slip
US stock index futures pointed to a lower opening on Friday as weak forecasts from Applied Materials and Nvidia weighed on the shares of chipmakers and Turkey’s battered currency slipped further.
Shares of Nvidia dropped 2.3 percent in premarket trading after the chipmaker said cryptocurrency-fueled demand had dried up and forecast current-quarter sales below Wall Street estimates.
Applied Materials slid 4.2 percent after the world’s largest supplier of chip equipment forecast current-quarter results below estimates, adding to fears that a two-year chip boom may be losing steam.
Micron fell 1.7 percent, while Intel slipped 0.3 percent. Dutch chip equipment maker ASML’s US-listed shares dropped 1.3 percent, while Lam Research fell 1.9 percent.
1.30pm update: Lira drops as Turkish court rejects appeal
The lira has dropped below 6.21 against the US dollar.
It comes after the Turkish newspaper, Haberturk, said that an appeal to release Mr Brunson from house arrest had been rejected.
12:00pm update: China gives support to Turkey
China has spoken out in support of Turkey following the threat of additional US sanctions.
China’s Foreign Ministry said Turkey can “overcome” the economic problems.
It said: “Turkey is an important emerging market country, and it remaining stable and developing benefits regional peace and stability.
“China believes that Turkey has the ability to overcome the temporary economic difficulties, and hopes the relevant sides can ease their differences via dialogue.”