Meanwhile, Pompeo noted that Brunson's detainment was just one of many issues the U.S. has with Turkey - for instance, Turkey's ongoing detention of three Turkish employees of the United States consulate in Istanbul.
US President Donald Trump and his Vice President Mike Pence had threatened Turkey with "large sanctions" last week if Brunson was not immediately released.
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.
Cavusoglu told Turkish press that the meeting was "constructive", but also spoke out against the sanctions.
The sanctions, announced Wednesday, allow the USA government to target individuals and companies involved in corruption or human-rights abuses, which in this case include Turkey's justice and interior ministers.
"Brunson needs to come home, as do all the Americans being held by the Turkish government", Pompeo told the press prior to his side meeting with the foreign minister at a Southeast Asian security conference.
"Pretty straightforward", Pompeo said.
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Turkey has said the sanctions were unacceptable.
Turkish President Recep Tayyip Erdogan said he will seek worldwide arbitration if the Trump administration fails to deliver the fighter jets.
Turkish Foreign Minister Mevlut Cavusoglu was quoted by media Friday as saying that Ankara was preparing to respond to Washington in equal measures.
He added: "We are going to work to see if we can find a way forward; I am hopeful that we can".
On Wednesday, the White House announced that it was imposing sanctions on Turkish Justice Minister Abdulhamit Gul and Interior Minister Suleyman Soylu.
Brunson, who was put under house arrest last month, faces a prison sentence of up to 35 years if convicted.
Under the sanctions to be imposed by the Treasury Department, any property, or interest in property, belonging to Justice Minister Abdulhamit Gul or Interior Minister Suleyman Soylu within USA jurisdiction would be blocked.
Erdogan has denied speculation that there had been an agreement to swap Brunson for Turkish citizens being held overseas, particularly 27-year-old Ebru Ozkan.