Flags across CT are being lowered to half-staff in honor of the five Capital Gazette newspaper employees killed by a gunman who attacked their newsroom.
Buckley had said Monday that the White House had declined the initial request the mayor submitted through Maryland's congressional delegation.
The White House says Trump ordered the flags be lowered as soon as he learned of the Annapolis mayor's request. White House press secretary Sarah Sanders Tuesday said that the initial rejection of the request didn't come from the president himself.
At a news conference in Annapolis on Tuesday, Buckley said the city will keep Annapolis flags at half-staff until the victims of the attack have been buried.
Buckley has issued a statement saying he appreciates the president lowering the flags and recognizing the tragedy of the shooting.
"Americans across the country are united in calling upon God to be with the victims and to bring aid and comfort to their families and friends".
Buckley told The Baltimore Sun Monday: "Obviously, I'm disappointed, you know?".
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Shortly after the order was released Tuesday, Buckley told the Sun that the reversal was "the least respect we could give the journalists". "This was an attack on the press. It's just as important as any other tragedy", said Buckley.
In fact, Buckley's request may not have been denied so much as delayed.
According to the U.S. Flag Code, the national flag may be ordered lowered only by the president or the governor of a state - though the governor may only do so if the deaths being commemorated directly affected that state.
Gov. John Kasich has ordered flags at public buildings and grounds in the state flown at half-staff in honor of five newspaper journalists slain in Maryland's capital.
Mr Trump repeatedly has called journalists the "enemy of the people".
"At this point in time, it would start to polarise people and I don't want to make people angry", Mr Buckley, 55, who moved to the United States in 1992 and has become a successful restaurant owner in Annapolis, said. More recently, it flew at half-staff after 10 people were killed at a high school in Santa Fe, Tex.