The UN report groups Saudi Arabia with other countries accused of gross violations against children, including Syria and Sudan, and extremist groups such as ISIS and Boko Haram.
In the first public comment by Saudi Arabia on the report, UN Ambassador Abdallah Y. Al-Mouallimi said his nation exercised "the maximum degree of care and precaution to avoid civilian harm."
The Saudi diplomat blamed the Houthi rebels in Yemen for the violence against children, declaring their actions as "heinous acts."
'We are communicating'
Last year's draft report initially listed Saudi Arabia
, a move that enraged the Kingdom and led to fierce lobbying and even threats to withhold funding to the UN. Saudi Arabia was eventually dropped from the list.
Now, under a different UN secretary-general, this latest report holds the Saudi coalition responsible for 38 verified incidents of attacks on schools and hospitals in 2016.
At the news conference Friday, Saudi Arabia was somewhat more accepting of the UN conclusions.
"Relations between Saudi Arabia and the United Nations are very strong and I hope they will continue to very strong and I hope that they will continue to be cooperative, joint basis," Al-Mouallimi said.
Al-Mouallimi said the Saudi-led coalition in Yemen should not be listed at all "because we are conducting activities there in accordance with international legitimacy and in accordance with international law and in accordance with Resolution 2216.
This year's report differentiates between parties that have not "put in place measures during the reporting period aimed at improving the protection of children" and those that have.
Perhaps as a compromise, the UN included Saudi Arabia in the latter category, saying that it is trying to improve when it comes to violence against children in Yemen.
Al-Mouallimi told reporters: "We are communicating with them. And I hope we can overcome this issue by mutual understanding."
The United Arab Emirates' mission to the United Nations issued a statement supporting Saudi Arabia's position on the report.
"The Mission affirms that the UAE stands firmly aligned with the Kingdom of Saudi Arabia and the rest of the Coalition in rejecting the inaccurate information and statistics in the Secretary-General's report. The Coalition is committed to the protection of all civilians in armed conflict, particularly children," it said.
Earlier Friday, the leader of the UN's effort to prevent attacks on children said the Saudi coalition casualty totals are "still unacceptable" despite falling rates.
The secretary-general's special representative for children and armed conflict, Virginia Gamba of Argentina, reflected on the thousands of children behind the numbers of the UN report.
"What we are seeing today is they are at the center if the dynamic of violent conduct. They are the expendable commodity of conflict today," Gamba said.
Amnesty International accused the UN of caving in to political pressure by "watering down" the Saudi coalition's "grave violations of international law" and including it in a new category "specifically designed to limit condemnation of the coalition."
But Human Rights Watch praised the inclusion of Saudi Arabia in the report.
"The Secretary-General has done the right thing by including the Saudi-led coalition on his list of shame for the continuing attacks that have killed hundreds of children and destroyed dozens of schools and hospitals in Yemen" said Jo Becker, Human Rights Watch advocacy director.
The report says 1,340 children in Yemen have been killed or seriously injured. The UN says the Saudi coalition has informed the international body of measures taken in 2016 to reduce the impact of the conflict on children, including through their rules of engagement and the establishment of a joint incident assessment team.
In a statement, the UN said the "shocking levels of killing and maiming and use of denial of humanitarian access is a serious concern for the Secretary-General."
"The tragic fate of child victims of conflict cannot and must not leave us unmoved," Gamba said in the statement
"A child killed, recruited as a soldier, injured in an attack or prevented from going to school due to a conflict is already one too many," she said.
The conflict in Yemen began in early 2015, when Houthi rebels -- a minority Shia group from the north of the country -- drove out the US-backed government led by President Abdu Rabbu Mansour Hadi and took over the capital of Sanaa.
The crisis escalated into a multi-sided war which allowed al Qaeda and ISIS -- other enemies of the Houthis -- to grow stronger amid the chaos.
The Houthis are backed by Iran; a coalition led by Saudi Arabia has conducted air raids on the country in support of Hadi's government.