By Steve Holland

NEW YORK (Reuters) - (This story corrects sixth paragraph to say Matt Schlapp was White House political director, not deputy.)

Dozens of former appointees of the administration of former President George W. Bush announced their support for Republican presidential nominee Donald Trump on Sunday in a bid for party unity ahead of Trump's first debate with Democrat Hillary Clinton.

The Bush family and many connected to it remain cool to Trump. Former President George H.W. Bush reportedly plans to vote for Clinton in the Nov. 8 election while his Jeb, a former Trump rival, has said he will not vote for Clinton or Trump. George W. Bush has avoided the presidential race while helping raise money for Republican congressional candidates.

But a number of former Bush appointees have decided to endorse Trump, the New York businessman who is in a tight race with Clinton and is to debate her one-one-one at Hofstra University on Monday night in Hempstead, New York.

Fifty former Bush appointees were on a list of people described as founding members of a coalition of Bush alumni supportive of Trump. The list was provided by a Republican official close to the Trump campaign.

The list included former White House press secretary Ari Fleischer, former U.S. Attorney General John Ashcroft, former Labor Secretary Elaine Chao, former Treasury Secretary John Snow and former Health and Human Services Secretary Tommy Thompson.

The list also included former Defense Secretary Donald Rumsfeld, former Veterans Affairs Secretary Anthony Principi and former White House political director Matt Schlapp, who is chairman of the American Conservative Union.

Thompson, in a statement, explained his decision to be on the list.

"Americans want to trust our leaders again, to know that they are fighting for everyday Americans by creating jobs, growing our economy, defending our nation from terrorism, and respecting the voters enough to be straight-forward and honest with them," Thompson said.

Trump has struggled to rally many in the Republican Party behind him. On Friday, he received the endorsement of former rival Ted Cruz, but many establishment figures remain skeptical about him, such as Ohio Governor John Kasich.

(Reporting By Steve Holland; Editing by Robert Birsel and Bill Trott)