Hagai Amir has been serving a 16-year sentence since 1996 for complicity in the killing of Rabin by his brother, Yigal Amir.
Hagai Amir told prison officials in 2004 that he could have Sharon killed by making a phone call, according to court documents.
"What are you afraid of? That I will murder or assassinate Sharon?" he said, according to the documents. "I can have Sharon killed with a single phone call."
Hard-line nationalists opposed Sharon's plan to withdraw from the Gaza Strip, completed in September.
According to the documents, Hagai Amir claimed he made the first statement sarcastically, and never made the second threat at all. He accused prison guards of conspiring against him.
He is to be sentenced on the latest charge Feb. 13. It was not immediately clear how much additional time he could face.
Yigal Amir is serving a life sentence for murdering Rabin after a peace rally in Tel Aviv in 1995.
Sharon suffered a massive stroke Jan. 4 and remains comatose in a Jerusalem hospital.
Meanwhile, acting Israeli Prime Minister Ehud Olmert huddled with top military and political officials Sunday to discuss the growing likelihood that the militant group Hamas could dominate this week's Palestinian elections.
The ascendance of Hamas has alarmed Israel, which appears to have been caught off guard by the group's surging popularity before Wednesday's vote. Hamas has killed hundreds of Israelis in suicide bombings and remains committed to Israel's destruction.
"What Israel has to do is the big question," Cabinet minister Tzachi Hanegbi said before Sunday's meeting. "We have to think hard and explore all the options."
Israel's Western allies also have been scrambling to figure out how to deal with Hamas. U.S. officials confirmed Sunday they have been directing money to promote democratic parties in the election but denied the move was aimed against Hamas.
Hamas, best known for its suicide attacks, has won over the Palestinian public in its first run for the legislature by focusing on domestic concerns, halting government corruption and restoring law and order to the chaotic West Bank and Gaza Strip.
In contrast, the ruling Fatah Party has been unable to shed its corrupt image or overcome infighting. Recent opinion polls show the two movements running neck-and-neck.
Olmert met with his Cabinet and later with a smaller group of senior officials to discuss the vote. Participants included the army chief, head of the Shin Bet security agency, and the justice and defense ministers, Olmert's office said.
Olmert appointed a committee headed by military chief Lt. Gen. Dan Halutz to monitor the elections and develop recommendations for responding to the election.
While some security officials privately support a dialogue with Hamas, top leaders, including Halutz and Defense Minister Shaul Mofaz, say the group must disarm and revoke its charter calling for Israel's elimination.
"Regarding the elections in the Palestinian authority, there are three options: that Fatah wins, that Hamas wins or anarchy wins. One of these results could put all progress back several years," Halutz told an academic conference Sunday, apparently referring to Hamas and warning that violence could follow the election.
Commentators said Sunday's meeting reflected a failure by Israel to detect Hamas' growing popularity, despite its strong performance in Palestinian municipal voting in recent months.
"Their assumption was Fatah will handily win any election," said Mouin Rabbani, an analyst with the International Crisis Group based in Jordan.
In an interview televised Sunday, Abbas defended his decision to allow Hamas to run in the election. Abbas has said he hopes Hamas would tame its positions once it formally joins the political system.
But other Fatah officials sent mixed signals over whether they would work with the Islamic group. Palestinian Information Minister Nabil Shaath, a top Fatah official, said Hamas must accept the principle of peace with Israel if it wants to share power.
"With Hamas, it will be very difficult to reach a joint program," Shaath added. "We can't form a coalition with Hamas if it doesn't agree to this program."
However, Fatah's top candidate, jailed Palestinian uprising leader Marwan Barghouti, said Sunday that "Hamas will be part and parcel of the Palestinian Authority" after the vote. Barghouti was interviewed in an Israeli prison by the Arab satellite TV station Al-Jazeera.
The United States and European Union also are trying to figure out what to do if Hamas ends up dominating the Palestinian parliament.
While supporting Hamas' right to run in the election, the United States and EU both consider Hamas a terrorist group, and both have said millions of dollars in aid to the Palestinians could be jeopardized.
"As a matter of policy, we don't deal with Hamas," said Stewart Tuttle, the U.S. Embassy spokesman in Tel Aviv. "If Hamas members win seats ... we are not going to deal with those individuals."
The U.S. Agency for International Development has used a special $1.9 million budget to promote democratic parties in the Palestinian election, said a U.S. Consulate spokeswoman in Jerusalem, Micaela Schweitzer-Bluhm.
She denied that the money, used in part to clean streets, distribute free food and water and to help fund a youth soccer tournament, was used to boost Fatah's prospects against Hamas.
Behind the scenes, U.S. officials are considering the possibility of distinguishing between Hamas legislators tied to violence and those who are not — a position Israel rejects. European diplomats said they would only decide what to do after election results are in.
Palestinian officials said security forces will begin a mass deployment Monday to ensure order during the election.
The West Bank and Gaza Strip have been plagued by a wave of chaos and lawlessness in recent months, and some armed groups have threatened to disrupt the voting.
Interior Minister Nasser Yousef said he gave "tough orders" to his forces "to stop any display of arms during the election day."
In other developments, an Israeli aircraft fired at three Palestinian gunmen trying to infiltrate into Israel from the Gaza Strip, killing one man and wounding two others, according to the army and Palestinian officials. The Popular Resistance Committees, a tiny militant group not running in the election, vowed revenge.