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.
Before his move home last week, Brunson, who led a Protestant church in the Aegean city of Izmir, had spent almost two years in jail.
Speaking to Turkish journalists after the meeting, Cavusoglu also described the discussion with Pompeo as "constructive", but added: "Nothing can be achieved through threatening language and sanctions".
The case is now at the centre of a bitter row between North Atlantic Treaty Organisation allies Ankara and Washington after the U.S. on Wednesday imposed sanctions on the Turkish justice and interior ministers claiming they played a major role in the arrest and detention of the pastor.
After reports that the United States would sanction individuals over the case, the lira hit a record low of 5.01 against the dollar, before rallying slightly to 4.9. "But we have agreed to work together, closely cooperate and keep the dialogue in the coming period".
Following the meeting, State Department spokeswoman Heather Nauert said that Pompeo "had a constructive conversation" with Cavusoglu and they " agreed to continue to try to resolve the issues between our two countries".
Expertos: derogar ley cambiaria es positivo, pero "insuficiente"
Y sin una unificación de tasas las distorsiones se mantendrán, opina el diputado opositor José Guerra, exdirectivo del Banco Central .
"Brunson needs to come home, as do all the Americans being held by the Turkish government", Pompeo told reporters before the meeting.
Pompeo met with Turkish Foreign Minister Mevlut Cavusoglu on the sidelines of a Southeast Asian security conference in Singapore.
"They've been holding these folks for a long time".
Wraps and salads sold at Kroger, Walgreens recalled due to parasite concern
The alert says some beef, pork and poultry salad and wrap products were sold at stores like Kroger, Trader Joe's and Walgreens . The complete list of products , product labels, the UPC code numbers and other identifying information can be found below.
On the sanctions, he said: "I hope they'll see this for what it is, a demonstration that we're very serious". "These are innocent people".
The sanctions targeting Justice Minister Abdulhamit Gul and Interior Minister Suleyman Soylu freeze any property or assets on U.S. soil held by the two ministers, and bar USA citizens from doing business with them.
Turkey has said the sanctions were unacceptable.
Facebook Shutters More Fake Accounts, Believed to Be Linked to Russian Federation
Their statement reads: "We face determined, well-funded adversaries who will never give up and are constantly changing tactics ". Some of those fake accounts included pages like " Aztlan Warriors ", "Black Elevation", "Mindful Being", and " Resisters ".
Andrew Brunson, who has lived in Turkey for two decades, was swept up in a string of arrests in the wake of a failed military coup against Mr. Erdogan in 2016.