In his first public remarks about the uproar, Ban said he decided to take the coalition off the list after Saudi Arabia along with other Arab and Muslim countries threatened to cut off funding to UN humanitarian programs.
"It is unacceptable for member-states to exert undue pressure," Ban told reporters at UN headquarters.
"Scrutiny is a natural and necessary part of the United Nations."
The United Nations had blacklisted the coalition after concluding in a report released a week ago that it was responsible for 60 per cent of the 785 children killed in Yemen last year.
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The UN chief has been under fire from rights groups who charged that he had caved in to Saudi pressure and damaged the credibility of the United Nations.
"This was one of the most painful and difficult decisions I have had to make," Ban said.
Confirming reports of a threatened cut-off of funding, Ban said he "had to consider the very real prospect that millions of other children would suffer grievously if, as was suggested to me, countries would de-fund many UN programs."
"We did not use threats or intimidation and we did not talk about funding," said Mouallimi.
A Security Council diplomat earlier said 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.
"I stand by the report," Ban said, warning that "the content will not change."
The UN chief appealed to member-states to defend the reporting mechanisms such as the children in armed conflict annual blacklist.