On Wednesday, Duterte said the ICC "is being utilised as a political tool against the Philippines".
Presidential spokesman Harry Roque confirmed that Mr Duterte has instructed Executive Secretary Salvador Medialdea to issue the notice.
Should the Philippines withdraw from the court it would not be the first to do so, as Burundi became the first nation to leave in October 2017.
8 started a preliminary examination of a complaint filed by a Philippine lawyer accusing Duterte and top officials of crimes against humanity committed during a war on drugs that has killed thousands of people.
"Even if the process progresses to the investigation proper, he will be accorded his right to contest the charges, or even disclaim the Court's jurisdiction to try him".
The letter dated March 15, 2018 said that the decision to withdraw from the Rome Statute was because of the Philippines' "principled stand against those who politicize and weaponize human rights".
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The Philippines is a signatory to the Rome Statute, a multilateral treaty that created the worldwide court.
The announcement of the investigation by the ICC was premature and implied he had already been charged for serious crimes, Duterte said.
"The membership of the Philippines in the system is essential for the aspirations toward universal ratification of the Rome Statute and strengthening the worldwide rule of law", it added.
ACT Teachers Party Rep. Antonio Tinio however said Duterte is not yet off-the-hook on the investigation of the global court even after he declared the withdrawal of the Philippines from the treaty.
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In response to Duterte's decision, a majority of the Philippine senators signed a resolution declaring that termination or withdrawal from the agreement is only "valid and effective" with their consent.
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"There appears to be a concerted effort on the part of the United Nations special rapporteurs to paint me as a ruthless and heartless violator of human rights who allegedly caused thousands of extrajudicial killings", Mr Duterte said.
In contrast with the contention of the Office of the President, Centerlaw contended that there is no further requirement of publication in any newspaper of general circulation "to make the treaty binding upon the Philippines".
On Monday, local media reported that the Philippine Senate had filed a resolution saying the country's withdrawal from global treaties would only be valid with its consent.
The Duterte administration, however, had the option of remaining a signatory while challenging the jurisdiction of the ICC, specifically under Article 19, by proving that "it is investigating or prosecuting the case or has investigated or prosecuted".
Last month, the ICC formally opened a "preliminary examination" as a potential prelude to a full-fledged investigation of accusations of crimes against humanity vis-à-vis senior Filipino officials, including Duterte. How could it counter the criticisms that the war on drugs is mainly targeting the poor?
Under the treaty, withdrawal is only effective one year after a country gives written notice of its decision to the United Nations secretary-general.
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Bishop Ruperto Santos of Balanga, however, said the Philippines is sovereign and independent and whoever commits a crime "should be tried here with our people".