Housing Minister Effie Eitam, leader of the National Religious Party (NRP), called the planned evacuation of 21 Gaza settlements ethnic cleansing.
"We are about to transfer thousands of Jews from their homes and to create a Hamas, and Jihad and Hezbollah independent state on the blood of innocent Jews," he said.
Jewish settlers in the Gaza Strip say their answer to Sharon's plan to dismantle their communities is to build more.
"We continue the daily life, and we accelerate the action of construction and absorbing new families," said a settler.
While the Palestinian Authority would welcome an Israeli withdrawal from Gaza, it is angry that it's been shut out of negotiations by Israel.
"Unfortunately, we've seen the Israeli government negotiating (with) its coalition, negotiating (with) the Likud, negotiating (with) the United States, and the side whose future is concerned with these plans have not even been consulted," said Palestinian Cabinet Minister Saeb Erekat.
CBS News Correspondent Robert Berger reports Israel refuses to negotiate with the Palestinian Authority on grounds that it is involved in terrorism.
With Eitam's exit, Sharon no longer commands a majority in parliament, but his opponents don't appear to have enough votes to bring him down.
Sharon is expected to court the opposition Labor Party, a former coalition partner and more comfortable ally for his plan to withdraw Israeli soldiers and about 7,500 settlers from Gaza by the end of 2005.
The prime minister has said he is determined to forge ahead, despite stiff opposition from hardliners, including leading members of his Likud Party.
Last week, Sharon fired the pro-settler National Union, one of three coalition partners, to assure a Cabinet majority for the Gaza plan.
In its session Sunday, the Cabinet agreed in principle to withdraw from Gaza and four small West Bank settlements in four stages by the end of 2005 — the first time an Israeli government has endorsed the idea of dismantling veteran settlements in the West Bank or Gaza.
However, as the price for support from senior Likud ministers, Sharon agreed to have the Cabinet approve each stage of settlement removal.
This was not enough for Eitam, a fiery ex-general who took control of the NRP last year and rejects all territorial compromise with the Palestinians.
"This government and prime minister must be removed from power," Eitam told a news conference after submitting his resignation Tuesday. A fellow party hardliner, deputy minister Yitzhak Levy, also resigned, telling Sharon in his resignation letter "the flag of the Land of Israel has been lowered to half-mast in your time."
Eitam and Levy said they would join the parliamentary opposition and vote against Sharon's government in no-confidence motions on Monday. The remaining four NRP legislators have not yet decided, but at least two indicated they would stay to try to scuttle the dismantling of settlements from a position of influence.
Sharon's Likud and his main partner, the centrist Shinui Party, have 55 seats in the 120-member parliament. The resignations of Eitam and Levy leave the coalition with only 59 members.
However, Labor has pledged to give Sharon a "safety net" by abstaining in no-confidence votes against him. With Labor staying on the sidelines — as it did in voting Monday — it would be very difficult for Sharon's opponents to bring him down. In order to remove him from office, they would have to garner 61 votes and agree on an alternate candidate for premier.
Some see the Labor promise as the first step toward recreating the Likud-Labor government that served in Sharon's first term, from 2001 to 2003.
Labor backs a withdrawal from Gaza, but some Labor stalwarts are skeptical about Sharon's will to carry it out. Until recently, Sharon was the leading champion of settlement construction and expansion.
In another development, Israel announced Tuesday it would close the joint Israeli-Palestinian industrial park at the Erez crossing point between Gaza and Israel. The closure would idle 4,000 Palestinian workers, a severe setback for the impoverished coastal strip.
The park has been open only sporadically during more than three years of violence. Palestinian militants have carried out several attacks on Israeli guards at the park, and workers often could not reach their jobs because of Israeli security restrictions. Israeli factory owners complained that they could not keep their businesses open under such conditions.
Trade Minister Ehud Olmert said the factories would be moved to cities in southern Israel, creating job opportunities for many unemployed Israelis there.