(CNN) The White House has rejected a Turkish offer to release an American pastor in exchange for forgiveness of billions of dollars in US fines on a Turkish bank, expressing that other matters would be considered only after Andrew Brunson is released, a senior administration official told The Wall Street Journal .

The rejection could lead to the US imposing additional sanctions against Turkey sometime this week, the Journal reported. Treasury Secretary Steven Mnuchin said Thursday that the United States is willing to do so if Brunson isn't released.

"A real NATO ally wouldn't have arrested Brunson in the first place," the senior White House official told the Journal, referring to Turkey's membership of the North Atlantic Treaty Organization.

Worsening relations

Brunson has been held in Turkey since 2016 , accused of helping to plot a coup attempt against Turkish President Recep Tayyip Erdogan.

The North Carolina native's case has rapidly soured relations between Washington and Ankara, with the two sides trading increasingly heated rhetoric and retaliatory tariffs.

On Friday, a Turkish high criminal court rejected Brunson's appeal to be released from house arrest and allowed to travel abroad after his appeal was rejected by a lower court.

Later that day, Trump tweeted , "Turkey has taken advantage of the United States for many years. They are now holding our wonderful Christian Pastor, who I must now ask to represent our Country as a great patriot hostage. We will pay nothing for the release of an innocent man, but we are cutting back on Turkey!"

An evangelical pastor, Brunson has lived in Turkey for more than 23 years with his wife and three children, according to the American Center for Law and Justice (ACLJ), an organization led by attorney Jay Sekulow that has advocated for his release.

But in October 2016, several months after a failed coup attempt in Turkey, Brunson was arrested and accused of plotting to overthrow the Turkish government.

He was formally indicted in March on charges of espionage and having links to terrorist organizations. The charges against Brunson include supporting the outlawed Kurdistan Workers' Party as well as the Gulen Movement, which Turkey says orchestrated the coup attempt.

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Earlier this month, Trump doubled steel and aluminum tariffs on Turkey , in what administration officials said was a move to punish Ankara for a lack of progress in bringing about Brunson's release.

The US has also slapped sanctions against Turkey's ministers of justice and interior over the issue, and both Trump and Vice President Mike Pence have taken up Brunson's case with Turkish officials.

Tensions in the Turkey-US relationship have been steadily ratcheting up for weeks, even as the NATO allies cooperate on other fronts, perhaps most importantly coordinating over the US air base in Incirlik, Turkey.

In an op-ed in The New York Times earlier this month, Erdogan criticized the US over its actions in the Brunson affair, its reaction to the coup attempt two years ago and its alliance with the People's Protection Units, or the YPG, the fighting group in Syria that Turkey asserts is a branch of the Kurdistan Workers' Party, labeled a terror group by the US.

"Before it is too late, Washington must give up the misguided notion that our relationship can be asymmetrical and come to terms with the fact that Turkey has alternatives," Erdogan said. "Failure to reverse this trend of unilateralism and disrespect will require us to start looking for new friends and allies."