Ban's decision to take the coalition off the list of child rights violators triggered a storm of protest from rights groups who charge the UN chief caved in to Saudi pressure and damaged the world body's credibility.
In his first public remarks about the uproar, Ban said he took the "painful and difficult" decision when he faced the "very real prospect" that millions of children would suffer if countries de-funded many programs.
"It is unacceptable for member-states to exert undue pressure," Ban told reporters. "Scrutiny is a natural and necessary part of the United Nations."
The United Nations blacklisted the coalition after concluding in a report released a week ago that it was responsible for 60 percent of the 785 children killed in Yemen last year.
But in an embarrassing climbdown for the United Nations, Ban announced on Monday that the coalition would be scratched from the list of shame pending a joint review with the Saudi-led alliance.
Saudi Ambassador Abdullah al-Mouallimi denied that his government had put pressure on the United Nations to reverse its decision by threatening to cut off millions of dollars in funding.
"We did say that such a listing and such unfair treatment would obviously have an impact on relations," said Mouallimi.
"But we did not use threats or intimidation and we did not talk about funding," he added.
UN officials and Security Council diplomats confirmed that the Saudis had "whipped up a lot of supporters" to pressure Ban to make the changes, and threatened in particular to withdraw funding from the Palestinian relief agency UNRWA.
Saudi allies weigh in
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The Saudis enlisted their allies in the Arab League, the Organization for Islamic Cooperation and the Gulf Cooperation Council to wage a full-on campaign for the list to be changed.
The coalition launched an air campaign in support of Yemen's President Abedrabbo Mansour Hadi in March 2015 to push back Huthi rebels after they seized the capital Sanaa and many parts of the country.
The war has killed some 6,400 people, with more than 80 percent of the population in desperate need of humanitarian aid, according to the United Nations.
Speaking to reporters after Ban's statement, the Saudi ambassador maintained that the decision to withdraw the coalition from the list was "final, irreversible and unconditional."
Ban said he stood by the report and warned that "the content will not change."
He acknowledged that "the impression is not a good one" from the decision to de-list the coalition, but he argued that there were more important issues at stake.
"Because of this, you can't burn down the whole house," he said.
UN spokesman Stephane Dujarric said the Saudi and Yemeni governments were fully briefed on the content of the report in March, rejecting claims by the Saudi ambassador that Riyadh was not consulted.
The UN chief appealed to member-states to defend the reporting mechanisms used by the world body such as the children in armed conflict annual blacklist.
The blacklist was established by a Security Council decision in 1999, but the council has been silent on the dispute over the coalition's listing.
The controversy over adding the Saudi-led coalition to the blacklist followed a similar uproar last year over the decision to exclude Israel over the deaths of 500 children in the war in Gaza.