Brunson faces up to 35 years in jail on charges of carrying out activities on behalf of two terror organisations - the group led by US-based Fethullah Gulen blamed for the July 2016 failed coup and the Kurdistan Workers' Party (PKK).
President Recep Tayyip Erdogan has said he has asked Turkish authorities to freeze the assets in Turkey of the USA ministers of "justice and interior", in response to Washington's sanctions over the detention of an American pastor.
Erdogan's remarks came after Turkish Foreign Minister Mevlut Cavusoglu and US Secretary of State Mike Pompeo met on the sidelines of a summit in Singapore on Friday and described the meeting as "constructive".
Turkey has said the sanctions were unacceptable.
"Of course you can't expect all issues to be resolved in a single meeting", he said.
Brunson was in a Turkish prison for 21 months until he was transferred to house arrest last week.
On Friday, the two leaders agreed to work together to resolve tensions between the two countries.
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Erdogan said Turkey will never step back from defence industry projects, saying 48 out of the 400 projects are related to the defence industry.
The move is created to put the Turks on notice that the "clock had run out" and that it was time for Pastor Brunson to be returned home, Pompeo said.
On the sanctions, he said: "I hope they'll see this for what it is, a demonstration that we're very serious". "They've been holding these folks for a long time".
The United States has also been seeking the release of three locally employed embassy staff detained in Turkey. "These are innocent people", he said.
"We've seen no evidence that Pastor Brunson has done anything wrong and we believe he is a victim of unfair and unjust detention by the government of Turkey", White House Press Secretary Sarah Huckabee Sanders emphasized to reporters Wednesday.
"I am instructing my friends today, we will freeze assets, if there are any, of the U.S. justice and interior secretaries in Turkey", Erdogan, speaking at a ruling Justice and Development (AK) Party meeting in Ankara, was quoted as saying by the official Anadolu news agency.
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.