The Australian Mayor of Annapolis says he is disappointed US President Donald Trump declined to order American flags be lowered to half-mast across the US to honour the five employees shot dead at The Capital Gazette newspaper.

Perth-raised Gavin Buckley, elected Annapolis Mayor last year, submitted the flag request to the White House over the weekend.

Mr Trump ordered flags be lowered for recent mass shootings at Florida and Texas high schools, but declined for the tragedy in Annapolis, Maryland.

Five Capital Gazette staff members were shot dead at their office in Annapolis, Maryland. ( Twitter: Capital Gazette )

"Obviously, I'm disappointed," Mr Buckley, who moved to the US in 1992, told the Baltimore Sun.

"Is there a cut-off for tragedy?

"This was an attack on the press. It was an attack on freedom of speech."

"It's just as important as any other tragedy."

Sorry, this video has expired Multiple people killed in shooting at a Maryland newspaper, US

Maryland's Governor had ordered state flags to be lowered to half-mast, but last week Mr Buckley told the Baltimore Sun he thought The Capital Gazette shooting merited national recognition as well.

"It's not as noticeable when a state flag is down but you still have your main flags at full mast," he said after submitting his request.

"Obviously, this got a lot of national attention and the President knows about it."

Jarrod Warren Ramos, 38, is accused of walking into the office of the newspaper on Thursday and shooting dead five employees with a shotgun.

The attacker was arrested in The Capital's newsroom minutes after he opened fire. ( AP: Jose Luis Magana )

Ramos, who reportedly had a long-running dispute with the newspaper, was arrested in the newsroom just minutes after he opened fire.

The White House did not immediately respond to a request for comment.

Mr Buckley said his wife talked him out of pushing ahead without the President's approval and lowering flags in Annapolis, the capital of the US state of Maryland.

"At this point in time, it would start to polarise people and I don't want to make people angry," Mr Buckley said.

AAP/ABC