During its campaign against Iran-backed rebels in Yemen there have been repeated criticisms that coalition air strikes have not done enough to avoid non-military targets.
Rights groups have also raised concerns about civilian casualties caused by the Houthi rebels, but United Nations human rights chief Zeid Ra'ad Al Hussein said the coalition bore the greatest responsibility.
"Looking at the figures, it would seem that the coalition is responsible for twice as many civilian casualties as all other forces put together, virtually all as a result of air strikes," Zeid said in a statement.
"We are possibly looking at the commission of international crimes by members of the coalition."
His office said it had tallied just under 9,000 civilian casualties, including 3,218 killed, since the coalition on March 26 last year intervened to support President Abedrabbo Mansour Hadi after rebels seized large parts of Yemen including the capital Sanaa.
The Houthis are allied with elite troops loyal to former president Ali Abdullah Saleh.
Zeid voiced particular alarm at two air strikes on a market this week in northern Yemen's rebel-held Hajja province.
The UN children's agency on Thursday put the death toll from those strikes at 119, and Zeid's office said Friday that 106 of those killed in the crowded market were civilians, including 24 children.
UN Secretary General Ban Ki-moon demanded an investigation into the incident, one of the deadliest yet in the war.
During an exclusive interview on Wednesday the coalition spokesman, Brigadier General Ahmed al-Assiri, told AFP the strikes targeted "a militia gathering", the term he uses to describe Houthis.
Assiri said an independent panel was being formed nationally to examine charges of possible abuses against civilians in the war.
The alliance says it does not aim at civilians, and that targeting is verified many times to ensure non-combatants will not be killed.
Zeid's office condemned "the repeated failure of the coalition forces to take effective actions to prevent the recurrence of such incidents, and to publish transparent, independent investigations into those that have already occurred."
Assiri said the coalition itself has investigated various incidents and some of the findings have been released.
The latest controversy comes with the coalition "in the end of the major combat phase", according to Assiri, who said security stabilisation and then reconstruction would follow.
White House spokesman Josh Earnest said on Thursday that "we would welcome and do welcome" Assiri's comment about an end to major operations.
"We have expressed our concerns about the loss of innocent life in Yemen. The violence there that is plaguing that country has caught too many innocent civilians in the crossfire," Earnest said.
While the United States has provided logistical and intelligence support to the coalition, the White House has privately expressed anger about the loss of civilian lives.
US support includes targeting assistance, which officials say makes strikes less indiscriminate.
"The Yemen operation I think by all accounts has produced horrific costs and tangled the United States in this conflict," said Frederic Wehrey of the Middle East Programme at the Carnegie Endowment for International Peace in Washington.
There may now be "the start of a recalibration" but the proof will lie in what happens on the ground, he said.
"They've done these announcements before," Wehrey told AFP.
Last April, Saudi Arabia announced an end to its initial air strikes in Yemen, dubbed "Decisive Storm", and a Saudi newspaper proclaimed "Mission Accomplished".
But the war has continued, with coalition forces providing training, equipment and guidance to Yemen's army, backed by the coalition air support, Assiri said.
Anti-rebel forces have retaken territory, including much of the south, but have failed to dislodge the Shiite Houthi rebels from Sanaa or to completely remove them from the country's third city Taez where intense battles continue.
Mustafa Alani, of the independent Gulf Research Centre, said that although fighting is not necessarily going to finish by March 26 "the operation is basically reaching its end".
He said the coalition was keen "not to go beyond that psychological date."