We will ban its judges and prosecutors from entering the United States.
Among other potential repercussions, Bolton threatened to pursue sanctions against ICC officials if the court moves forward with investigations into U.S. citizens.
Ms. Bensouda submitted a formal request to start an investigation based upon a 2016 ICC report that found that USA armed forces and the Central Intelligence Agency might have committed war crimes by allegedly torturing detainees. Although the US does not recognize Palestinian statehood, the PLO has maintained in Washington a general delegation office that facilitates Palestinian officials' interactions with the USA government.
The second area Mr Bolton addressed was the Palestinian move to bring U.S. ally Israel before the ICC over allegations of human rights abuses in Gaza and the occupied West Bank - a move dismissed by Israel as politicised. And Bolton added, "We will not allow the ICC, or any other organization, to constrain Israel's right to self-defense", per the Wall Street Journal.
"We will not cooperate with the ICC".
The national security adviser said the closure of the Palestine Liberation Organization's office would not impact the U.S. administration's ongoing Arab-Israeli peace plan.
Husam Zomlot, head of the PLO General Delegation to the United States, described on Monday the decision as reckless: "We condemn in the strongest terms the USA administration's decision to close the Palestinian mission to the US".
Senior Palestinian official Saeb Erekat told reporters in Ramallah that the full range of political, economic and security ties would be reassessed in the wake of the Trump administration's decision on Monday to shut the Palestinian mission in Washington.
It added: "This decision is also consistent with administration and congressional concerns with Palestinian attempts to prompt an investigation of Israel by the global criminal court".
Israel welcomed the Trump administration's move and accused the Palestinians of seeing the court as a way of sidestepping US-sponsored bilateral talks. The Palestinians accused the administration of dismantling decades of US engagement with them. Erekat said the Palestinians will continue to push for that, which Nauert also cited as a reason for the US decision to shut down the office. Palestinian officials say the reason given for the closure was their campaign at the ICC.
Bolton said on Monday that the U.S. will impose sanctions on court officials who attempt to investigate either the United States or Israel.
Under President George W. Bush, the United States did not ratify the Rome Treaty that established the ICC in 2002. We will provide no assistance to the ICC. And we certainly will not join the ICC.
In a separate statement, the court's overseeing body, the Assembly of States Parties (ASP) also pointed out that the ICC "recognises the primary jurisdiction of States to investigate and prosecute atrocity crimes".
Last November Palestinian Authority President Mahmoud Abbas used his speech at the United Nations to call for the investigation and prosecution of Israeli officials by the International Criminal Court (ICC). Bush's Democratic successor, Barack Obama, took some steps to cooperate with it.
Bolton also announced the Trump administration is closing the Palestine Liberation Organization office in Washington, D.C. The PLO called the move a risky escalation, saying it shows "the U.S.is willing to disband the worldwide system in order to protect Israeli crimes and attacks against the land and people of Palestine, as well as against peace and security in the rest of our region".