Dagan's comments Sunday during a symposium on regional strategy at the Hebrew University in Jerusalem, the first time he has publicly opposed military action against Iran, challenged hard-line Prime Minister Binyamin Netanyahu.
That has made it more difficult for Netanyahu to press the case for an attack with his own Cabinet, with Washington or with the Israeli public.
Dagan's broadside also sharpened a simmering national debate on whether Israel should take pre-emptive military action to prevent Iran acquiring nuclear weapons at a time when the Islamic Republic is seeking to extend its influence across the Middle East.
Netanyahu has vowed he will never allow Iran to threaten Israel's existence with nuclear arms.
That pledge, and the mindset behind it, constantly alarmed U.S. President George W. Bush, no pussycat when it came to playing rough, because he feared such action would ignite a regional war.
President Barack Obama has also sought to dampen Israeli ardor for military action to eliminate what Netanyahu sees as an existential threat to Israel that challenges its nuclear monopoly in the region.
Some military commanders are also reluctant to launch attacks on Iran, and the issue has caused sharp divisions within the defense establishment.
Indeed, recent embarrassing intrigues over the selection of a new military chief of staff, which spilled over into the public domain, hinged on candidates' positions on the Iran issue.
In April diplomatic cables from the U.S. Embassy in Tel Aviv, released by WikiLeaks, revealed that in 2007 Netanyahu expressed a willingness to join the government of Prime Minister Ehud Olmert if Israel initiated an attack on Iran.
Olmert's coalition, under heavy fire following the Israeli military's poor performance in the 2006 war against the Iranian-backed Hezbollah of Lebanon, was falling apart, and he was exploring the possibility of a unity government with Netanyahu's Likud Party.
Netanyahu is backed by Defense Minister Ehud Barak, a former chief of staff and Israel's most decorated war hero.
In January Barak even ditched his Labor Party, which generally opposed attacking Iran. That forced Labor ministers out of Netanyahu's coalition, effectively burying the party that founded the state of Israel.
Barak even cut short the tenure of Lt. Gen. Gabi Ashkenazi as chief of staff in 2010 after the general bluntly objected to a proposal to attack Iran, which he reportedly said "will only bring disaster upon Israel."
"Without Barak by his side," the liberal Haaretz daily observed recently, "Netanyahu would find it hard to advance aggressive moves on the Iranian front.
"Netanyahu has no military record that grants him supreme defense authority, as Ariel Sharon had. Only Barak, with his ranks and medals, his seniority as a former prime minister, can give Netanyahu this kind of backing."
The fissures within the Israeli leadership cadre continue to widen, as Dagan's uncompromising comments Sunday underlined.
Dagan, who in January retired as director of the Mossad, Israel's foreign intelligence service, has long had a reputation for daring clandestine operations.
During his eight-year term in Mossad he was widely seen as being behind a series of covert operations that damaged Iran's nuclear program, either by sabotaging the uranium enrichment process, assassinating nuclear scientists or luring them into defecting.
Even so, he says Israel should go on employing the disruptive tactics he has used to sabotage the Iranian effort rather than unleash air or missile strikes.
"An airstrike on the nuclear facilities is a dumb idea," he told the Jerusalem symposium. "It's important to remember that war is only one option among many alternatives."
Washington's focus on diplomatic action, such as sanctions, to isolate Iran infuriates Netanyahu, to the point that in February he called for "credible military action" against the Islamic Republic.
Meantime, analysts say Israel's offensive options are narrowing as Iran fortifies its nuclear facilities.
"While an Israeli attack in the next six months is highly unlikely," Oxford Analytica noted, "the country will soon have to decide whether to go it alone before it is too late, or to rely increasingly on untested U.S. willingness to use its much more powerful forces."