The statement was immediately denounced by the Palestinian leadership, which said it was the thinking of the mafia, not a government.
It also reinforced unusual questioning of the security strategy of the Israeli prime minister, Ariel Sharon, from within the country's political establishment, amid a growing belief that his insistence on a military solution to the conflict is costing Israeli lives.
At the weekend, Shimon Peres, the former prime minister and present leader of the opposition Labour party, broke a long silence on criticising the government's security policies by warning Mr Sharon that the decision to "remove" Mr Arafat by exiling him, or any other method, would help the militant Islamist movement Hamas.
"This government has destroyed the peace process," Mr Peres said on the 10th anniversary of the Oslo accords that won him a Nobel prize.
Mr Olmert told Israel radio that the cabinet's decision to remove Mr Arafat could be viewed in the same manner as Mr Sharon's pledge to wipe out the leadership of Hamas.
"Killing is definitely one of the options," he said. "We are trying to eliminate all the heads of terror, and Arafat is one of the heads of terror."
The statement was immedi ately condemned by the Palestinian chief negotiator, Saeb Erekat. "This is the thinking of the mafia," he said.
The Palestinian leadership has found unusual backing on the issue from within the Israeli political mainstream, which has until now shied away from drawing a link between Mr Sharon's security policies and terrorist attacks.
But Labour's doubts turned to anger when Mr Sharon was seen to undermine a seven-week ceasefire by the continued killing of Hamas and Islamic Jihad leaders. The truce brought a lull in the suicide bombings, but the army's resumption of "targeted killings" provoked what the two groups said were retaliatory suicide bombings that left more than 30 people dead.
The chairwoman of the Labour faction in parliament, Dalia Itzik, told a party meeting chaired by Mr Peres at the weekend that Mr Sharon was sacrificing Israeli lives. "The prime minister has failed completely and must resign."
The leftwing Meretz party also condemned the threat to Mr Arafat as endangering Jewish lives and strengthening Hamas. "If you deport Arafat you leave the ground only for Hamas," it said. "That's not something the government is doing out of stupidity. It's a strategy to keep things as they are, to prevent the solution of two states."
The mainstream press has been unusually critical, describing the move as evidence of a "bankrupt policy".
