The White House announced an immediate review of Washington's support for the 18-month-old military push after planes hit mourners at a community hall in the capital, Sanaa, on Saturday, killing 140 people, according to one UN estimate and 82 according to the Houthis.
The statement from Riyadh's main ally, noting for the second time in as many months that US support was not "a blank check", sets up an awkward test of a Saudi-US partnership already strained by differences over wars in other Arab lands.
The reproach also indirectly hands a propaganda win to Riyadh's arch-rival, Tehran, a Houthi ally that has long seen the Sunni kingdom as a corrupt and domineering influence on its impoverished southern neighbour, diplomats say.
Sources in the Saudi-led coalition denied any role in the attack, but Riyadh later promised an investigation of the "regrettable and painful" incident, with U.S. expert advice. The move was apparently aimed at heading off further criticism of a military campaign already under fire for causing hundreds of civilian deaths in apparently indiscriminate attacks.
"There will be pressure on the campaign," said Mustafa Alani, a security analyst close to Saudi Arabia's Interior Ministry. While the coalition followed very careful rules and understood human rights concerns, "there will now be pressure to end the whole operation, or to restrict the operation".
An estimated 10,000 people have been killed in the war and the United Nations blames coalition strikes for 60 percent of some 3,800 civilian deaths since they began in March 2015.
The outcry over civilian casualties has led some lawmakers in the United States and Britain as well as rights activists to push for curbs on arms sales to Riyadh, so far without success.
The coalition denies deliberately targeting civilians and says it goes to great lengths to ensure its raids are precisely targeted, with explosive loads calibrated to limit the risk of causing damage beyond the immediate target area.
Saudi officials said the kingdom did not want to fight a war in Yemen.
"But we cannot stand by while insurgents overthrow a legitimate government in a neighbouring state by force, while Yemen becomes a lawless state and terrorist haven, and while we are attacked across our border," one of the officials said.
"Saudi Arabia will continue to provide military support to Yemen’s legitimate government while the insurgents continue their illegal campaign. ... But we will also continue to support and promote a negotiated settlement."
The coalition accuses the Houthis, who seized much of the north in a series of military advances since 2014, of placing military targets in civilian areas. The Houthis deny that.
Fury in Sanaa at Saturday's raid was echoed internationally.
A spokesman for UN Secretary-General Ban Ki-moon said any deliberate attack against civilians was utterly unacceptable.
Ban called for "a prompt and impartial investigation of this incident. Those responsible for the attack must be brought to justice", the spokesman said.
Iranian Foreign Minister Mohammad Javad Zarif said in a letter to Ban that the Saudi-led coalition and those who had supported it should "be held accountable for the war crimes perpetrated in Yemen over the past year and a half."
Yemen and Saudi Arabia blame Shi'ite Iran for supplying weapons to the Houthis. Tehran views the Houthis, who hail from a Shi'ite sect, as the legitimate authority in Yemen but denies it supplies them with weapons.
UN emergency relief coordinator Stephen O'Brien described the attack as obscene and heinous. France called it a "massacre" and said it wanted an independent inquiry.
There was dismay, too, in the ranks of the internationally recognised Yemeni government that the coalition is defending.
"It's shocking to see that a target like this was hit," said a senior official in the Saudi-backed government of President Abd-Rabbu Mansour Hadi. "It's the latest in a series of attacks by all sides on civilian targets like homes and public gatherings that are turning this into a dirty war."
"If anything positive can come from this, it would be increasing the will for a ceasefire that is needed. But incidents like these before have just fuelled a desire for revenge."
Yemen's powerful former president, Ali Abdullah Saleh, a key Houthi ally, called on Sunday for an escalation of attacks against Saudi Arabia, demanding "battle readiness at the fronts on the (Saudi) border".
Saleh's remarks reflected the febrile political climate in Sanaa, but it was not clear what concrete effect they might have. Houthi forces regularly fire rockets across the frontier, occasionally killing or wounding Saudi civilians, and bands of Houthi fighters stage border incursions almost daily.
Thousands of Yemenis, many of them armed, gathered at the UN headquarters in Sanaa on Sunday calling for an international investigation into the strike.
The funeral wake was for the father of the interior minister of northern Yemen's Houthi-run administration, Jalal al-Roweishan, who died of natural causes on Friday. Yemenis say the Roweishan family is widely respected and has good ties with many groups and tribes across Yemen's political spectrum.
Mokhtar al-Rahabi, a spokesman for Hadi, condemned the attack on his official Facebook page on Saturday.
"Bombing a mourning hall in which there were dozens of civilians is not acceptable, even if leaders of the (Houthi) putschists were present. Our war is a war of morals."
A statement issued by the alliance after Saturday's raid reiterated that its forces "have clear instructions not to target populated areas and to avoid civilians".
But the eventual prospect of a more limited military campaign - perhaps through tighter targeting parameters for air operations - and a possible reduction in Western support could deliver a blow to Riyadh's efforts to confront perceived Iranian expansionism in its southern neighbour.
The Houthis and powerful local allies hold most of Yemen's northern half, while forces working for the exiled government share control of the rest of the country with local tribes.
Peace talks have made little headway. Hadi's government insists on compliance with U.N. Security Council resolution 2216, which calls on the Houthis to withdraw from cities seized since 2014.
Riyadh has long accused Hezbollah's ally Iran of backing the Houthis and seeking to transform the group into a replica of the Lebanese militia to use as a proxy against Saudi Arabia.
While Washington has long expressed understanding for Saudi concerns about Iranian activism in Arab lands, the US military has distanced itself from the coalition's targeting decisions.
In June, the US military withdrew personnel from Saudi Arabia who were coordinating with the Saudi-led air campaign, and sharply reduced the number of staff elsewhere who were assisting in that planning.
US officials, speaking on condition of anonymity, said the lower staffing was not due to concern over civilian casualties. But the Pentagon also said that in its discussions with the coalition, it pressed the need to minimize civilian casualties.