They group did so in an open letter, released first to The Washington Post, Censor.NET reports.
The letter takes issue with Trump statements that appear to question the alliance, encourage Russia to hack and release Hillary Clinton's deleted State Department emails, and seem to recognize Russia's annexation of Crimea, which the United States considers illegitimate.
"These are disgraceful statements that betray our long-standing values and national interests embraced by presidents of both parties," said the letter, signed by former secretary of state Madeleine Albright and former CIA director and defense secretary Leon Panetta.
"We find Trump's comments to be reckless, dangerous, and extremely unwise. They contradict a core, bipartisan principle found in every U.S. administration - that our security in North America is indivisible with our democratic allies in Europe."
Signatories include Ian Brzezinski, who was deputy assistant secretary of defense for Europe and NATO policy in George W. Bush's first term; Damon Wilson, a top NATO and European affairs adviser to Bush; and Randy Scheunemann, a neoconservative foreign policy figure.
The letter does not endorse Clinton or mention her apart from the email issue. Many of the Democrats who signed on to the letter have separately endorsed Clinton, as has at least one of the Republican signatories, foreign policy expert Kori Schake.
Trump's offhand call last week for Russia to find and release emails Clinton had deleted from her private server marked the start of a rocky period for Trump that has left some Republicans despondent. Clinton allies see Trump's unorthodox foreign policy pronouncements as a prime opportunity to pick up Republicans unable to stomach Trump.
"A solemn obligation of the American president is to lead NATO, to remain resolute in defense of our allies and to convince potential adversaries that we will stand up for NATO without fear or reservation," the letter said.
"Every president, without exception, has accepted the wisdom of this strategy. That is why we find Trump's cavalier denigration of NATO so worrying and so objectionable. Strong alliances are essential to U.S. national security. America needs a president who will strengthen our alliances, not denigrate and destroy them."
Related materials: Occupation of Crimea