The letter, first reported by The New York Times
Monday, warns: "We are convinced that in the Oval Office, he would be the most reckless President in American history."
Its signatories include former CIA and National Security Agency Director Michael Hayden, former Director of National Intelligence and Deputy Secretary of State John Negroponte and Eric Edelman, who was Vice President Dick Cheney's national security adviser and has worked closely with Michele Flournoy -- a candidate for secretary of defense in a prospective Clinton administration -- to forge a centrist group of defense experts on key military issues.
It also includes two Homeland Security secretaries under Bush, Tom Ridge and Michael Chertoff, and Robert Zoellick, a former World Bank president, U.S. trade representative and deputy secretary of state.
Trump's campaign responded with a statement from Trump denouncing the signatories as people who deserve the "blame for making the world such a dangerous place."
Many of the same leaders wrote an open letter in March
during the Republican primaries condemning Trump and pledging to oppose his candidacy, at a time when other GOP candidates remained in the race.
The letter acknowledges that many Americans "have doubts about Hillary Clinton, as do many of us."
"But Donald Trump is not the answer to America's daunting challenges and to this crucial election," it says.
In the new letter, the group warns Trump "lacks the temperament to be President."
"He is unable or unwilling to separate truth from falsehood. He does not encourage conflicting views. He lacks self-control and acts impetuously. He cannot tolerate personal criticism. He has alarmed our closest allies with his erratic behavior," the letter claims. "All of these are dangerous qualities in an individual who aspires to be President and Commander-in-Chief, with command of the U.S. nuclear arsenal."
The idea of writing such a letter had been discussed by GOP national security officials for a while, but gained momentum when Trump called on Russia to share Clinton emails it potentially hacked and when he took a position many saw as legitimizing Russia's claim to Ukraine's Crimea region.
"We thought it was important to make the point that even for longtime Clinton critics, Trump poses too big a risk to short- and long-term national security," one person involved with the letter said.
It was drafted by John Bellinger, a former State Department legal adviser to then-Secretary of State Condoleezza Rice, with edits from Bob Blackwill, a former George H.W. Bush White House adviser, and Eliot Cohen, also a former adviser to Rice.
Bellinger told CNN the letter was circulated five days ago with very few changes.
"People were in different places about whether they want to endorse Clinton and their doubts about her, but we settled on a statement that recognizes many people have concerns about Clinton," he said. "Some people will clearly endorse her, others will never endorse her, but everyone was united in their belief that Donald Trump is not qualified."
Bellinger said he wanted to focus on gathering signatures from very high-level people -- several cabinet secretaries, numerous deputies and many dozen assistant secretaries and White House staff that worked directly with the president.
"We wanted to get the most senior people we could: household names, of people who have worked in the Situation Room and know what is required of the president," he said. "I wanted almost every name to be familiar to those who follow the issues and who could speak with first-hand knowledge of what requires to be president. "
Another official who signed the letter told CNN that most signatories travel abroad and interact with current and former world leaders. Many were alarmed at how many world leaders said they were concerned that Trump's "recklessness" would invite America's enemies to be even more reckless.
This official said he was stunned by how "enthusiastic" everyone was to sign.
Trump has met with other GOP foreign policy bigwigs, including former secretaries of state Henry Kissinger and James Baker. Neither signed the letter.
"The names on this letter are the ones the American people should look to for answers on why the world is a mess, and we thank them for coming forward so everyone in the country knows who deserves the blame for making the world such a dangerous place. They are nothing more than the failed Washington elite looking to hold onto their power, and it's time they are held accountable for their actions," Trump said in a statement.
"These insiders -- along with Hillary Clinton -- are the owners of the disastrous decisions to invade Iraq, allow Americans to die at Benghazi, and they are the ones who allowed the rise of ISIS. Yet despite these failures, they think they are entitled to use their favor trading to land taxpayer-funded government contracts and speaking fees."
A senior Trump adviser sought to tie the letter's signatories to Clinton, saying: "Crooked Hillary and the rest of the Washington insiders are going to try to stop this grassroots effort at every turn."
"They're on the wrong side of history," the adviser said. "They're the ones launching a political attack ... and they have to own up to their role in putting the world in the place that it's in right now."