Abbas leads Palestinians in the West Bank but has no power in Gaza
Foreign Minister Avigdor Lieberman has questioned the authority of Palestinian leader Mahmoud Abbas in an escalating Israeli-Palestinian war of words.
Mr Lieberman said Mr Abbas "was not exactly legitimate" and was therefore in no position to make demands on the Israeli leadership.
A day earlier Mr Abbas had called him a bad choice as Israeli foreign minister.
The two sides have been unable to agree terms for restarting peace talks since the Israel government came into office.
Israeli Prime Minister Benjamin Netanyahu, who has been in power since 1 April, on Sunday urged Mr Abbas to restart peace talks immediately.
"There is no reason Palestinian Authority Chairman Mahmoud Abbas and I should not meet, anywhere in this country, to advance the political process," Mr Netanyahu told the weekly meeting of his cabinet.
Mr Abbas has refused to meet Mr Netanyahu and on Sunday reiterated his stance in a radio interview that, for negotiations on the key issues to resume, there must be "a complete halt" to Israeli settlement activity in the occupied West Bank.
Separately in the Egyptian weekly, October, he said that Mr Netanyahu had backed himself into a corner on the Palestinian track, and he would face fierce opposition from Mr Lieberman if he tried to emerge from it.
Mr Abbas said things would be better if the former Israeli foreign minister, Tzipi Livni, had been reappointed instead of the current incumbent.
The outspoken Mr Lieberman said he took such comments from Mr Abbas, also known as Abu Mazen, as a "blessing".
"As Abu Mazen's authority or legitimacy deteriorates or declines, he raises his demands and toughens his position.
"Abu Mazen isn't exactly legitimate, hence neither is his new demand, or suggestion, to replace Lieberman with Tzipi Livni," he said in an interview on Israel radio.
"I see such advice as a blessing. His demand to cease settlement construction is nothing more than an expression of his distress and incompetence."
He said that with Gaza under control of the Hamas militant group, Mr Abbas represented "at best, half of the nation".
Mr Lieberman also rejected a call by outgoing EU foreign policy chief Javier Solana for the United Nations to recognise a Palestinian state if Israel and the Palestinians fail to reach a peace agreement by a certain deadline.
"With all due respect to Solana, he's about to retire ... and we should not overstate the importance of his statement," Mr Lieberman said.
On Sunday, Mr Netanyahu insisted the Palestinians "must finally abandon" the right of return for Palestinian refugees since 1948, which if realised would facilitate the arrival of millions of displaced Arabs to areas that currently have an Israeli Jewish majority.
He reiterated demands for Palestinians to explicitly recognise Israel as a Jewish state, calling this "the key to peace."
The Palestinians say it is tantamount to legitimising their own displacement in past wars with Israel.
They have also rejected any potential deal between Israel and its main backer, the US, to allow limited Jewish settlement activity in the occupied West Bank.
"There are no middle-ground solutions for the settlement issue: either settlement activity stops or it doesn't," negotiator Saeb Erekat told Voice of Palestine radio.
Some 500,000 Israelis live in the West Bank and East Jerusalem, areas captured by Israel in 1967. Israel wants to be able to keep building within existing communities there, although all such work is illegal under international law.
"If settlement continues, Israel will be allowed to build 1,000 units here and 2,000 units there, which will lead Arabs and Palestinians to believe the US administration is incapable of swaying Israel to halt its settlement activities," Mr Erekat said.