Bolton's comments reinforced an earlier statement by the US Department of State which announced the closure of the office of the General Delegation of the Palestine Liberation Organisation (PLO) in Washington.
America's long-running reluctant relationship with the International Criminal Court came to a crashing halt on Monday as decades of US suspicions about the tribunal and its global jurisdiction spilled into open hostility, amid threats of sanctions if it investigates USA troops in Afghanistan.
Palestinian leaders confirmed they'd been informed by the Trump administration that it plans to shut the Palestinian mission in Washington, condemning the move as proof the U.S.is disbanding worldwide efforts toward a peace deal with Israel.
Potential measures include barring ICC judges and prosecutors from entering the U.S. and freezing any funds they have in the United States.
The Trump administration has exited three of Obama's signature global-governance achievements: the Trans-Pacific Partnership Agreement, the Paris Agreement, and the Iran deal.
The Palestinians said they were undeterred from going to the ICC.
"Any U.S. action to scuttle ICC inquiries on Afghanistan and Palestine would demonstrate that the administration was more concerned with coddling serial rights abusers - and deflecting scrutiny of U.S. conduct in Afghanistan - than supporting impartial justice", said Human Rights Watch.
In the wake of April bloodshed on the Gaza-Israel border, the court opened a preliminary probe to determine whether war crimes may have been committed by Israel, Hamas or other parties in the Palestinian territories since 2014.
"The Trump administration will not keep the office open when the Palestinians refuse to take steps to start direct and meaningful negotiations with Israel", he added.
"To the contrary, PLO leadership has condemned a United States peace plan they have not yet seen and refused to engage with the USA government with respect to peace efforts and otherwise", the statement added. "We will not cooperate with the ICC".
Although the USA does not recognise Palestinian statehood, the Palestine Liberation Organization (PLO), which formally represents Palestinians, has maintained a "general delegation" office in Washington.
The Palestine Liberation Organization, commonly known as the PLO, formally represents all Palestinians.
UNRWA was founded after the 1948 war surrounding Israel's creation to serve some 700,000 Palestinians who fled or were uprooted from their homes.
The administration's move to close the PLO office in Washington is not directly connected to the Trump White House's opposition to the International Criminal Court, although the administration is trying to link them.
The ICC, which is based in the Hague, has a mandate to prosecute war crimes, crimes against humanity and genocide.
The fate of the Georgetown offices has been in limbo for over a year, ever since the administration discovered it was congressionally obligated to close the diplomatic facility should Palestinian officials target Israel at the International Criminal Court.
"These people have made a decision to stand on the wrong side of history by protecting war criminals and destroying the two-state solution", responded Palestinian chief negotiator Saeb Erekat. The U.S. has notified the Palestinians it's closing their mission, September 10, 2018, the latest in a series of American blows to the Palestinians.
"Rather than imposing sanctions, the United States should instead once and for all reaffirm its signature of the Rome Statute establishing the ICC, and support - not impede - its investigations".
Palestinian officials criticised the decision as another betrayal that effectively ends Washington's role as an impartial mediator in the decades-long conflict.