Mr Bozdag said Turkey did not hesitate to work together with any country who defended "correct principles" on Syria.
"Whoever defends what is right, we are on their side", he added in televised comments.
Earlier on Saturday, the United States, joined by Britain and France, struck a number of targets in Syria in response to the alleged chemical attack in the Eastern Ghouta's Douma district last week.
"No", Bozdag said, adding that Turkey "has different policies to Iran and Russian Federation".
The relationship between the United States and Turkey is likely to come under pressure as long as a US pastor remains in jail, a USA official responsible for worldwide religious freedom said on Monday.
Jacqueline Furnari, Brunson's daughter, told NBC News her father has been pulled into a "political game between Turkey and the U.S". Assad's main supporters are Moscow and Tehran. In a meeting previous year with his Turkish counterpart, U.S. President Donald Trump asked that the government "expeditiously" return the pastor to the U.S. But the appeals have not made much headway.
Also, Rex Tillerson, former secretary of state, told Erdogan in February that USA prosecutors had dropped charges against most members of his security detail who had been accused on playing a role in beating protesters a year ago, the Wall Street Journal said.