Abbas' spokesman, Nabil Abu Rdeneh, rejected Lieberman's statement, calling it an "incitement to violence" that "doesn't contribute in any way to an atmosphere of peace." He urged Israel and the international community to condemn the letter.
Elections for new Palestinian leadership were scheduled for 2010, but have repeatedly been delayed because of the bitter dispute between Abbas' Fatah and the militant Hamas, bitter rivals who had a violent falling out in 2007 and now separately govern the West Bank and Gaza Strip respectively.
Israeli Prime Minister Benjamin Netanyahu also sought to quickly disassociate himself from the letter. An official in the prime minister's office, who spoke on condition of anonymity because of the sensitivity of the issue, said the letter does not represent the government's position.
"While Abbas has created difficulties for restarting negotiations, the government of Israel remains committed to continuing efforts to restart a dialogue with the Palestinians," he said.
Lieberman, who leads a hardline party in Israel, is known for inflammatory rhetoric that has at times agitated his partners in government.
He embarrassed Netanyahu in the past by expressing skepticism over the chances of reaching peace with the Palestinians. In a high-profile speech at the United Nations General Assembly in 2010, he contradicted a goal set by President Barack Obama of reaching a final peace deal in the coming year.
Lieberman wrote that Abbas should be replaced so that peace talks that collapsed in 2008 could be revived.
Abbas has refused to resume talks as long as Israel refuses to stop settlement construction in the West Bank and east Jerusalem, areas Palestinians want as part of their future state. Israel rejects the calls for a halt to settlement building, and instead has called for peace talks to resume, saying that the settlement issue should be resolved along with other core disputes through negotiations.
Lieberman listed in his letter a number of gestures Israel recently has made to the Palestinians including agreeing for an additional 5,000 Palestinians to work in Israel and reducing the number of roadblocks and accused Abbas in return of "encouraging a culture of hatred, praising terrorists, encouraging sanctions and boycotts and calling into question the legitimacy of the state."
"Due to Abbas' weak standing, and his policy of not renewing the negotiations, which is an obstacle to peace, the time has come to consider a creative solution ... in order to strengthen the Palestinian leadership," Lieberman said.
In Washington, U.S. State Department spokeswoman Victoria Nuland said the U.S. has "a good working relationship with President Abbas. ... And so we expect to be able to continue to work well with him."
She also noted that Netanyahu had "clarified that the foreign minister's letter doesn't reflect his position and that [Netanyahu] has responsibility for these issues."