The PLO responded by accusing the United States of banding with Israel against the Palestinians to the detriment of the peace process.
The court "has been ineffective, unaccountable, and indeed outright dangerous", he said.
Mr. Bolton's remarks specifically referenced a move made late last year by ICC prosecutor Fatou Bensouda to launch a probe into possible war crimes committed by the US and its allies during the 17-year-long war in Afghanistan.
The U.S. State Department said on Monday that the PLO has not taken steps to support the start of direct and meaningful negotiations with Israel. However, such a deal is unlikely given Palestinian mistrust of his administration.
He said the plan continued to be refined with an eye toward eventually proposing it. It also contends that the PLO is refusing to engage with the US government on peace efforts.
"While the court welcomes the membership of the so-called "State of Palestine", Bolton said during his speech at the Federalist Society.
Mr Bolton said the Palestinian move was one of the reasons the United States administration had chose to close the Palestinians' diplomatic mission in Washington.
PLO Secretary General Saeb Erekat said in a statement before the official announcement that "the rights of the Palestinian people are not for sale".
The Palestine Liberation Organization is the group that formally represents all Palestinians.
The Trump administration warned previous year that it might close the PLO office office after Palestinian Authority President Mahmoud Abbas called for the investigation and prosecution of Israeli officials by the ICC and other bodies.
"We lost the United States administration but we gained our national rights", said Zomlot, who was recalled back to Ramallah in the spring amid tensions between Washington and the Palestinian leadership.
A protester takes part in a demonstration against the USA funding cut to the UN Relief and Works Agency for Palestine Refugees in the Near East, in the Ramallah, the occupied West Bank, last week.
Over the weekend, it announced it was cutting $25m (£19m) in assistance for hospitals in east Jerusalem that provide critical care to Palestinian patients.
The U.S. has also moved its embassy from Tel Aviv to Jerusalem.
The International Criminal Court on Tuesday said its work would continue "undeterred" after Washington threatened to prosecute its officials if Americans are charged with war crimes committed in Afghanistan.
Reuters got their hands on an advanced copy of Bolton's speech, and it includes threats of sanctions against ICC judges and prosecutors, as well as a promise to "fight back"-whatever that means".
Bolton's draft text says the United States will not cooperate with the ICC, and that if it does investigate USA actions in Afghanistan then the Trump administration will consider travel bans, asset freezes and possible prosecution in US courts for the judges and prosecutors involved in the probe. The organization opened the office in 1994 and went on to join the ICC after receiving observer state status at the United Nations in 2012.
"So although the ICC has weaknesses and limitations, I still think we are better off as an global community to have it, than not to have it".
Bolton remained firm that the only institution United States recognised was its constitution and will not allow ICC to interfere with its affairs or those of her allies. Any countries supporting the investigation and cooperating with the ICC will be subject to secondary sanctions, Bolton warned. "After all, for all intents and purposes, the ICC is already dead to us", he said.
She said the Taliban and the Afghan National Security Forces, would also be investigated.
If such an inquiry goes ahead, the Trump administration will consider banning judges and prosecutors from entering the United States, put sanctions on any funds they have in the USA financial system and prosecute them in American courts, Bolton said.
The United States will enact a similar punishment on any company or state that assists the ICC.
"No committee of foreign nations will tell us how to govern ourselves and defend our freedom", he said.
The court added that it believes that US authorities ultimately ended the torture of detainees, which is why most of the alleged abuses happened in 2003 and 2004 when George W. Bush was commander-in-chief.