But his controversial comments have brought a swift insistence from the US that his pledge still stands.
"I said during in our first meeting about three years ago that I accepted his request not to harm (Yasir) Arafat physically," Sharon told Israel's Channel 2 on Friday.
"But I am released from this commitment. I release myself from this commitment regarding Arafat."
Sharon said he told this to Bush last week during a meeting with him at the White House, where he received US approval for his plan to unilaterally evacuate all settlements from the Gaza Strip and some in the West Bank.
The latest threat against Arafat comes a week after Israel assassinated Hamas chief Abd Al-Aziz al-Rantisi in a missile strike, and less than a month after the resistance group's spiritual leader Shaikh Ahmad Yasin was killed by the same way.
Those killings were condemned by most major governments with the exception of the US.
But the White House has bluntly insisted Sharon must abide by the past pledge not to harm Arafat.
"We have made it entirely clear to the Israeli government that we would oppose any such action and have done so again in the wake of these remarks," said a senior Bush administration official. "We consider a pledge, a pledge."
"This is an escalation and will lead to increased tensions"
Nabil abu Rdainah,
An adviser for Arafat
An adviser for Arafat, Nabil abu Rdainah, said Sharon's statement would lead to increased tensions in the region.
"We reject Sharon's statement and demand clarification from
Mr Bush on such a statement and hold Sharon responsible for
such a dangerous statement," he said. "This is an escalation and will lead to increased tensions."
When Sharon appeared to threaten Arafat on 2 April, US Deputy Secretary of State Richard Armitage told reporters: "Our position on such questions - the exile or assassination of Yasir Arafat - is very well known. We are opposed."