Albayrak's ministry said they had discussed US sanctions against Turkey and agreed to act together in responding to such moves and to boost cooperation between their countries.
Brunson, an evangelical preacher from North Carolina, is now under house arrest in Izmir.
The Trump administration has already sanctioned two Turkish leaders over the pastor's imprisonment.
Turkish authorities arrested Brunson in October of 2016 and accused him of being part of the attempted military coup earlier that summer.
The two countries have been locked in a heated crisis emanating from unjust sanctions and the actions of Trump, as Washington levied sanctions on Interior Minister Süleyman Soylu and Justice Minister Abdulhamit Gül for not releasing Brunson. "We haven't seen the last of that".
The Eye's report is based on comments from an anonymous diplomatic source.
The pastor's appeal had been rejected by a lower court and was sent to the higher court, Brunson's lawyer Ismail Cem Halavurt said, according to Anadolou.
Though Turkey's financial troubles did not originate with the battle over Brunson's release, the moves have sped up the Turkish economy's decline.
The tensions between Washington and Ankara escalated in July after Trump announced the USA will impose sanctions against Turkey as a result of the almost two-year-long detainment of Pastor Andrew Brunson.
Turkey's lira fell once again after the trade minister, Ruhsar Pekcan, said on Friday that her government would respond to any new trade duties, which Mr Trump threatened in his overnight tweet.
That much information was revealed by US Treasury SecretarySteven Mnuchin while addressing a cabinet meeting on Thursday when he said that the next spiral of tit-for-tat sanctions was coming soon, deepening a spat that has rattled financial markets, if Brunson is not released by Turkey. He called Brunson "a great patriot hostage". "We will pay nothing for the release of an innocent man, but we are cutting back on Turkey!" he tweeted.
Turkey's currency plummeted 20 percent against the greenback in a single trading day last Friday after President Donald Trump announced a doubling of steel and aluminum tariffs on Ankara, in return for the country's continued detention of American pastor Andrew Brunson.
The court in the western city of Izmir ruled that Brunson, who faces 35 years in jail if convicted, would remain under house arrest, his lawyer Cem Halavurt told AFP.
It may not sound as sexy, but eating carbohydrates in moderation may be best for boosting longevity, a large new study suggests. From age 50, the average life expectancy was an extra 33 years for people who ate carbs in moderation.
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His best shot over a final round of 4-under 66 was a lasered 4-iron to the 16th green that landed 6 feet away and set up a birdie. Over a wild first nine holes, Woods didn't hit a single fairway off the tee but got up and down from everywhere.
Both the World Health Organization and California state scientists have found links between the herbicide and cancer. It is also sprayed just before harvest on wheat, barley, oats and beans to kill the crop and allow earlier harvest.
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U.S. threatens more action against Turkey unless pastor freed
Turkey and Qatar - which is also a very close U.S. ally - have become close economic and political partners in recent times. Gallego said that Brunson's lawyer had indicated he would be willing to take his client's case to the constitutional court.
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Google employees push back on censored China search engine
Mr Pichai told staff Google's mission was to "organise the world's information". "China is one-fifth of the world's population". They said the project raised "urgent moral and ethical questions" and urged the firm to be more transparent.