It was only a single word — “legitimacy” — but in diplomatic parlance it’s a bombshell, a shot at the moral underpinnings of another government. When Hillary Rodham Clinton stood before television cameras last week to talk about Syria’s autocratic leader, not even her aides expected her to go that far.

And then she did.

“From our perspective, he has lost legitimacy,” the secretary of state said of Syrian President Bashar al-Assad.

The line, an unscripted response to a reporter’s question, was instantly hailed as a shift for the Obama administration, which until Monday had been relatively restrained in its public criticism of Assad. But while the White House had intended to sharpen its tone toward the Syrian leader, the decision to use the word was Clinton’s, according to two administration officials familiar with the incident.

Clinton’s utterance, coupled with Ambassador Robert Ford’s decision — also unscripted — to visit the opposition stronghold of Hama on July 7 , nudged the administration a step closer to declaring that Assad must step down. Taken together, the visit and Clinton’s remark show how the administration’s policy toward the Syrian autocrat has lately been shaped more by diplomatic improvisation than methodical planning within the White House.

With a single remark, Clinton put the administration more firmly on the side of protesters demanding Assad’s ouster, eliciting cheers from opposition groups and plaudits from former diplomats and Middle East experts who have pressed for a forceful repudiation of a government accused of killing more than 1,500 protesters since March. The calls for a harder stance increased after last week’s attack on the U.S. Embassy by a Damascus mob that smashed windows and pelted the building with fruit.

President Obama echoed Clinton’s phrase on Tuesday in a CBS News interview, though with a careful qualifier: “Increasingly you’re seeing President Assad lose legitimacy in the eyes of his people.”

The State Department’s activist approach highlighted divisions within the administration over the proper U.S. response to the crackdown. Some policy advisers, including senior members of Clinton’s staff, have cautioned against firm statements committing the United States to a policy of seeking Assad’s removal. There is no support internationally for a Libya-style military intervention in Syria, these advisers observe, and also little evidence that the country’s loosely organized opposition is prepared to take control of the country, raising the risk of prolonged turmoil or even civil war.

But after nearly four months of worsening violence and a string of broken promises by Assad, a growing faction within the administration began to urge a more assertive posture. These include Ford, the veteran diplomat and newly appointed ambassador to Damascus, as well as Clinton herself, who aides say reacted viscerally to reports of Syrian troops firing on peaceful demonstrators from tanks.

“She was disgusted,” said a senior administration official who attended high-level meetings on Syria. The official, who spoke on the condition of anonymity to discuss diplomatically sensitive deliberations, said Clinton was increasingly chagrined by the behavior of Assad, a Western-educated ophthalmologist who many White House and congressional officials had regarded as a potential reformer.

Like others in the administration, Clinton “thought at first that if we gave him some space, he would do the right thing,” the official said. “Instead, we see him using increasing brutality against his own people.”

A turning point, administration officials say, occurred July 10, when Assad had promised to meet with opposition leaders to begin a formal process of political reform. U.S. and European governments had been closely watching to see whether Assad would honor commitments to begin sincere negotiations, but they were quickly disappointed as Syrian police and army troops increased their attacks on protesters in several cities.

“People here are genuinely appalled that you have a government, you have a leader who claims to want a dialogue, but at the same time is overseeing a government that is practicing torture, terror, theft, firing upon people,” Jeffrey Feltman, assistant secretary for Near Eastern affairs, said in an interview Friday in Istanbul.

After Ford traveled to the restive city of Hama in an effort to discourage attacks on demonstrators there, the Syrian government retaliated by allowing the attack on the U.S. embassy by mobs of Assad supporters. Clinton’s declaration that Assad had lost his legitimacy occurred hours after the attack, although officials insisted the assault did not trigger Clinton’s comments.

“A bunch of clowns throwing fruit did not change our position,” said a second administration official involved in internal policy discussions.

By late last week, administration officials agreed on a plan to turn up the rhetorical pressure, however modestly, by declaring that Assad was “not indispensable” as Syria’s leader. The phrase was deliberately chosen to echo what U.S. officials say was a private boast Assad had made to foreign diplomats, claiming that his position as Syrian president was safe because U.S. and European leaders regarded him as “indispensable” in keeping ethnically divided Syria from fragmenting into chaos and possible civil war.

Clinton used the phrase at the start of a joint news conference Monday with European Union foreign policy chief Catherine Ashton.

“President Assad is not indispensable, and we have absolutely nothing invested in him remaining in power,” Clinton said.

Then, pressed by a reporter to clarify her views about Assad, she went off script. “I mean, from our perspective, he has lost legitimacy,” she added.

Former senior diplomats and Middle East experts praised the apparent policy shift.

“Up until now, it kind of looked like we were bending over backward not to be too critical,” creating an impression of a “double standard in the Middle East,” said John Negroponte, a former senior diplomat and U.N. ambassador.

Others chided the White House for taking caution to absurd extremes.

“If I had to describe the administration’s policy, I’d call it ‘The Late Show,’ ’’ said Elliott Abrams, a former top Middle East adviser to the George W. Bush administration. “They’re not being asked to sell arms to the Syrian protesters. They’re being asked to take a clearer moral and diplomatic stance.”

Late or not, Clinton has made clear that she does not regret the choice of words.

“We have said that Syria can’t go back to the way it was before,” she told reporters on Friday at a news conference in Istanbul. “Assad has lost his legitimacy in the eyes of his people because of the brutality of their crackdown, including today.”

Staff writer William Wan, traveling with Clinton, contributed to this report.