The former prime minister's position echoes that of the Turkish government.
The row over Mr Brunson escalated last week when US Vice President Mike Pence, like the pastor an evangelical Christian, said Turkey would face "significant sanctions" if this "innocent man of faith" was not freed.
Brunson, who ran a small church in Turkey for more than 20 years, was arrested in December 2016 over allegations of having helped a group that Ankara says was behind a failed military coup in July 2016.
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"We repeated this today", Turkish Foreign Minister Mevlut Cavusoglu said after he and US Secretary of State Mike Pompeo met on the sidelines of a regional security summit in Singapore.
The sanctions will freeze the United States assets of Turkey's minister of justice, Abdulhamit Gul, and its minister of interior, Suleyman Soylu. "Our relationship will never be cut", he said.
Two Turkish employees of United States consulates in Turkey are also now in jail on terrorism charges, and another is under house arrest, while several Americans have been caught up in the crackdown that followed a failed 2016 coup.
Erdogan, who is known for his sometimes provocative anti-Western rhetoric, has yet to comment.
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.
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His comments came two days after the US imposed sanctions on Turkey's Justice and Interior ministers over the detention of terror-linked USA pastor Andrew Brunson.
The standoff appears to be one of the most serious fallouts between the two North Atlantic Treaty Organisation allies in modern history, along with the rows over the 1974 Turkish invasion of Cyprus and the 2003 US-led invasion of Iraq.
Mr. Brunson had denied all charges and his case has become a cause celebre for US evangelicals and the Trump administration.
Berat Albayrak, Turkey's finance and treasury minister and President Recep Tayyip Erdogan's son-in-law, on Friday played down the idea that strains between the two countries would continue in the long term.
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The chosen astronauts will be the first to conduct flight tests and missions on the Boeing Starliner and Space X crew dragon . After that, the companies will become eligible for many years' and billions of dollars' worth of future NASA missions.