A settlers' spokesman, Yehoshua Mor-Yosef, said in a statement that bulldozers have begun leveling trailers at the Neve Erez South outpost.
Settler spokesman Ezra Rosenfeld called it appeasement.
"To give terror any kind of reward is a tragic mistake," he said.
Military sources said as many as 10 outposts could be removed by Tuesday morning, reports CBS News Correspondent Robert Berger. Media reports had said the military had drawn up a list of 14 or 15 settlement outposts, nearly all uninhabited, that are to be removed in coming days.
Earlier Monday, Palestinian prime minister Mahmoud Abbas said he will not use force against militant groups under any circumstances, despite their stated determination to derail a U.S.-backed peace plan with attacks on Israelis, including two weekend shootings that killed five soldiers.
The White House said the latest Palestinian attacks on Israel were a threat to peace and to the prospects for an independent Palestinian state, reports CBS News Correspondent Peter Maer.
Abbas also condemned the latest attacks, but said he would try to use persuasion, not force, to halt the attacks.
"There is absolutely no substitute for dialogue," Abbas said at his first news conference since taking office April 30, adding he still believes the armed groups would change their minds.
Abbas also defended himself against complaints at home that he has been too conciliatory to Israel, including in a speech at a Mideast summit last week, and that Israel has given little in return.
Abbas said he has coordinated every move with Yasser Arafat — a barb at the veteran leader who has said the summit yielded no achievements.
Army commanders met Monday with settler leaders, gave them the list of settlements to be removed and asked them to remove the outposts voluntarily or they would begin tearing them down as early as Monday night, according to Israel radio.
Settler leaders said they would not leave voluntarily, but would not violently confront soldiers.
"We won't lay a hand on (Israeli) soldiers. They're our brothers. We'll do everything to prevent a physical confrontation," said Mor-Yosef earlier. "If we are evacuated, we'll return the night after and establish 10 new outposts."
Under the road map, Israel has to dismantle dozens of outposts established since Prime Minister Ariel Sharon came to power in March 2001. According to the Israeli settlement watchdog group Peace Now, there are 102 outposts with about 1,000 residents, including 62 outposts built since Sharon took office.
Sharon, a major settlement builder in his career, never promised explicitly to remove all 62 outposts, and has acknowledged he has differences with the United States on the issue. His aides have said a distinction would be made between outposts considered legal and illegal, suggesting there would be less than full compliance.
The degree of resistance to the removal of isolated outposts will show how much of a fight settlers will put up in the event of a final peace deal, in which Israel would have to remove larger settlements.
About 220,000 settlers live in 150 settlements in the West Bank and Gaza, the lands occupied by Israel in the 1967 war and claimed b the Palestinians for their future state.
In the first stage of the peace plan, the Palestinians are required to disarm and dismantle militant groups that have killed hundreds of Israelis in the past 32 months of fighting.
Palestinian militias have said they will not halt attacks on Israelis, and last week announced they are stopping contacts with Abbas on a cease-fire.
The militants said Sunday's shootings, including a rare joint attack by three militias on an army outpost in Gaza, are meant to underscore their determination to derail the peace plan. Four soldiers were killed in the Gaza attack, and a fifth in an ambush in the West Bank city of Hebron later Sunday.
Palestinian officials, speaking on condition of anonymity, said the Egyptian intelligence chief, Omar Suleiman, is working to restart cease-fire talks. Suleiman presided over previous truce efforts earlier this year.
Abbas said Monday that he is pressing ahead with the peace plan. In veiled criticism of the militants, Abbas said: "The suffering of the Palestinians should not be dealt with by incitement. It needs real solutions."
However, there was no sign of compromise. Palestinians will not "surrender to the pressure exerted by Israel and the United States of America," Abdel Aziz Rantisi, a Hamas leader, said Sunday. "We are unified in the trenches of resistance."
There has been widespread grumbling among Palestinians that despite Abbas' moderate speech, Israel has not reciprocated. Palestinians had expected a quick easing of an Israeli travel ban and the lifting of other restrictions. However, the closure has remained in effect, in part because of renewed attacks by militants.