By Louis Charbonneau and Michelle Nichols

UNITED NATIONS (Reuters) - United Nations chief Ban Ki-moon said on Thursday that Saudi Arabia had exerted "unacceptable" undue pressure on the world body after a U.N. report blacklisted a Saudi-led military coalition for killing children in Yemen.

Riyadh had threatened to cut its funding of U.N. programs in response to the blacklisting last week and suggested a fatwa - an Islamic legal opinion - could be placed on the world body, Reuters reported on Tuesday.

The U.N. announced on Monday it had removed the coalition from its annual child rights blacklist pending a joint review by the organization and the coalition of child deaths and injuries during the year-long war in Yemen.

Ban described the decision as one of his most painful and difficult and said millions of other children likely would suffer if funding for U.N. programs was cut off.

"Children already at risk in Palestine, South Sudan, Syria, Yemen and so many other places would fall further into despair," he told reporters. "It is unacceptable for member states to exert undue pressure."

Ban did not specifically say the Saudis had threatened to cut off funding.

Saudi U.N. ambassador Abdallah Al-Mouallimi also reiterated his denials that Riyadh threatened Ban over the blacklist.

"It is not in our style, it is not in our genes, it is not in our culture to use threats and intimidation. We have the greatest respect for the United Nations institution," Mouallimi told reporters shortly after Ban spoke.

Diplomatic sources said Saudi Foreign Minister Adel al-Jubeir had called U.N. political affairs chief Jeffrey Feltman several times to complain about the report, which names states and armed groups accused of violating the rights of children during conflicts.

Mouallimi then met with Deputy Secretary-General Jan Eliasson on Monday.

The U.N. said Jordan, the United Arab Emirates and Bangladesh also contacted Ban's office to protest the listing of the coalition. Diplomats said Egypt, Kuwait and Qatar did likewise.

The Saudi-led coalition includes UAE, Bahrain, Kuwait, Qatar, Egypt, Jordan, Morocco, Senegal and Sudan.

One senior U.N. official described Ban's choice as between the "plague and cholera."

The United States backed Ban's remarks on Thursday and said the U.N. chief had invited the Saudis and coalition members to discuss the report in New York on June 17.

"The U.N. should be permitted to carry out its mandate, carry out its responsibilities, without fear of money being cut off," State Department spokesman Mark Turner told reporters.

RIGHTS GROUPS ANGRY

The Saudi-led coalition began a military campaign in Yemen in March last year with the aim of preventing Iranian-allied Houthi rebels and forces loyal to Yemen's ex-President Ali Abdullah Saleh from taking power.

Some 6,000 people, about half of them civilians, have been killed there since last March, according to the U.N.

The Houthis, Yemen government forces and pro-government militia have been on the U.N. child rights blacklist for at least five years and are considered "persistent perpetrators." Al Qaeda in the Arabian Peninsula is also on the blacklist.

Ban, who is in the final year of his second term and seen as a possible presidential candidate in his native South Korea, said a key concern of the Saudi-led coalition was that it had been listed alongside terrorist and extremist groups.

Human rights groups accused the U.N. chief of caving to pressure from powerful countries and said he risked harming his U.N. legacy.

Rights groups say the blacklist pressures warring parties to comply with international law, and that over the past 15 years some 20 governments and armed groups had taken steps to end violations of child rights in a bid to be removed from it.

The latest report blamed the Saudi-led coalition for 60 percent of the 510 child deaths and 667 injuries in Yemen in 2015. Ban said he stands by those figures, while Mouallimi has described them as "wildly exaggerated."

The annual report is produced at the request of the U.N. Security Council.

The 15-member council has not intervened in the controversy. It did not get involved last year when Israel and the Palestinian militant group Hamas were left off the blacklist after being included in an earlier draft.

Ban took a veiled swipe at the council on Thursday.

"When U.N. reports come under fire for raising difficult issues or documenting violations of law or human rights, member states should defend the mechanisms and mandates that they themselves have established," he said.

(Additional reporting by Lesley Wrougton in Washington; Editing by G Crosse and Paul Simao)