Brunson, who led a Protestant church in the Aegean city of Izmir, denies the charges. "However, Turkey always wishes to resolve these issues via diplomacy, dialogue and mutual understanding", Cavusoglu told reporters after meeting his USA counterpart Mike Pompeo in Singapore.
The government of President Recep Tayyip Erdogan "should seize the Trump Towers", Aytun Ciray, general secretary of the Iyi (Good) Party, said to protest the White House announcement of sanctions on Turkey's interior and justice ministers.
Also Turkish Foreign Minister said he told US Secretary of State Mike Pompeo that threats and sanctions will not work, after Washington targeted Turkish ministers over the detention of an American pastor.
Top diplomats from Turkey and the United States agreed on Friday to work towards a solution to the diplomatic spat that has erupted over the arrest of a USA pastor, which has already resulted in Washington slapping sanctions on Ankara.
Cavusoglu told Turkish press that the meeting was "constructive", but also spoke out against the sanctions.
"They've been holding these folks for a long time".
Turkish President Recep Tayyip Erdogan said he will seek worldwide arbitration if the Trump administration fails to deliver the fighter jets.
The White House imposed sanctions on Turkey earlier this week over the detention of Brunson, an evangelical pastor from North Carolina.
The Erdogan government has vowed to retaliate against the US sanctions, announced Wednesday, but has not revealed what they will be.
"We repeated to them that nothing can be achieved through threatening language and sanctions and we believe that this was well understood", Cavusoglu said.
On Wednesday, Washington moved to block the assets of Turkish Justice Minister Abdulhamit Gul and Interior Minister Suleyman Soylu in the United States and prohibit American citizens from "engaging in transactions with them".
"We are going to work to see if we can find a way forward", he emphasized.
Fifty-year-old Brunson faces up to 35 years in jail if convicted of carrying out activities on behalf of two groups, which Turkey considers to be terror organizations.
Mr Erdogan has previously tried to swap him for Fethullah Gulen, an Islamic cleric...