An open letter signed by 50 Republican national security experts has warned that nominee Donald Trump "would be the most reckless president" in US history.
The group, which includes the former CIA director Michael Hayden, said Mr Trump "lacks the character, values and experience" to be president.
Many of the signatories had declined to sign a similar note in March.
In response, Mr Trump said they were part of a "failed Washington elite" looking to hold on to power.
The open letter comes after a number of high-profile Republicans stepped forward to disown the property tycoon.
Mr Trump has broken with years of Republican foreign policy on a number of occasions.
The Republican candidate has questioned whether the US should honour its commitments to Nato, endorsed the use of torture and suggested that South Korea and Japan should arm themselves with nuclear weapons.
"He weakens US moral authority as the leader of the free world," the letter read.
"He appears to lack basic knowledge about and belief in the US Constitution, US laws, and US institutions, including religious tolerance, freedom of the press, and an independent judiciary."
"None of us will vote for Donald Trump," the letter states.
In a statement, Mr Trump said the names on the letter were "the ones the American people should look to for answers on why the world is a mess".
"We thank them for coming forward so everyone in the country knows who deserves the blame for making the world such a dangerous place," he continued.
"They are nothing more than the failed Washington elite looking to hold on to their power and it's time they are held accountable for their actions."
Also among those who signed the letter were John Negroponte, the first director of national intelligence and later deputy secretary of state; Robert Zoellick, who was also a former deputy secretary of state and former president of the World Bank; and two former secretaries of homeland security, Tom Ridge and Michael Chertoff.
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The letter echoed similar sentiment shared by some Republican national security officials in March, but the new additions came after Mr Trump encouraged Russia to hack Mrs Clinton's email server, according to the New York Times.
Mr Trump later said he was "being sarcastic" when he made the remarks about hacking his rival's emails.
Missing from the letter were former secretaries of state Henry Kissinger, George Shultz, James Baker, Colin Powell and Condoleezza Rice.
Some of the latest letter's signatories plan to vote for Mr Trump's Democratic opponent Hillary Clinton while others will refuse to vote, but "all agree Trump is not qualified and would be dangerous," said John Bellinger, a former legal adviser to Ms Rice who drafted the letter.
The open letter follows a fresh round of Republican defections in the wake of recent controversy surrounding Mr Trump.
Lezlee Westine, a former aide to President George W Bush, announced her support for Mrs Clinton in a statement to the Washington Post on Monday.
Wadi Gaitan, a prominent Latino official and chief spokesman for the Republican party in Florida, announced he would leave the party over Mr Trump's candidacy.
Meanwhile, George P Bush broke with his father, Jeb Bush, to lend his support to Mr Trump on Sunday, the Texas Tribune reported.
The Texas land commissioner urged party members to unite behind his father's former Republican primary rival.
Other Republicans not voting for Mr Trump
- Barbara Bush, former first lady
- Jeb Bush, former Florida governor, 2016 presidential candidate
- William Cohen, former secretary of defence
- Jeff Flake, Arizona senator
- Lindsey Graham, South Carolina senator, 2016 presidential candidate
- Larry Hogan, Maryland governor
- John Kasich, Ohio governor, 2016 presidential candidate
- Mark Kirk, Illinois senator
- Mitt Romney, former Massachusetts governor, 2012 Republican presidential nominee
- Ileana Ros-Lehtinen, Florida congresswoman
- Ben Sasse, Nebraska senator