Mr Erdogan told journalists on Sunday that the relationship between the two countries would be damaged if Washington persisted in what he described as "psychological warfare".
The US Vice President Mike Pence also took to Twitter to promise the pastor will always have the support of the American administration to ensure he is returned home, On Sunday he tweeted transferring Mr Brunson to home arrest was "just not good enough".
Brunson, a 50 year old evangelical pastor from Black Mountain, North Carolina, was arrested in December 2016 and later charged with links to a failed plot to overthrow the Turkish government in July 2016.
Israel reported Turkey had made a u-turn over a deal brokered by Mr Trump, in which the Jewish state would return a Turkish national accused of smuggling money to the militant group Hamas in exchange for Mr Brunson's freedom.
The United States will impose large sanctions on Turkey for their long time detainment of Pastor Andrew Brunson, a great Christian, family man and wonderful human being. He is suffering greatly. This innocent man of faith should be released immediately!— Donald J. Trump (@realDonaldTrump) July 26, 2018
However, Mr Erdogan denied any deal had been made to exchange Mr Brunson for Ebru Ozkan - a 27-year-old woman released by Israel earlier this month.
"We will not retreat because of sanctions," Mr Erdogan told Turkish journalists.
"We are not tied to the US with an umbilical cord. It should not forget that it stands to lose a strong and sincere partner," he told Hurriyet newspaper.
Brunson faces up to 35 years in prison for "committing crimes on behalf of terror groups" and espionage.
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