Netanyahu's opening of a public rift with his coalition ally appeared to be an attempt to minimize any diplomatic fallout at a time when Israel is trying to persuade world powers to ramp up sanctions against Iran over its nuclear activities.
In a letter to Catherine Ashton, the European Union's foreign policy chief, Lieberman accused President Mahmoud Abbas of "acting to undermine attempts to renew the peace process".
Lieberman urged the Palestinians to hold a long-delayed election to choose "a new, legitimate, hopefully realistic" leadership that can "bring progress with Israel".
Abbas was elected in 2005 and his original mandate expired in 2009. However, plans for a new ballot have been regularly postponed because of a deep schism within Palestinian politics.
Through an official in his office, Netanyahu swiftly distanced himself from Lieberman's comments. Lieberman heads the Yisrael Beitenu party, which holds 15 of the 66 seats that Netanyahu's coalition controls in the 120-member parliament.
"What was written in the letter by the foreign minister does not correctly represent the position of the prime minister or of the government as a whole," said the official, who declined to be identified by name.
"While the Palestinian leadership under Abu Mazen (Abbas) has created difficulties that have prevented the resumption of talks, Israel is committed to working with the Palestinian leadership to restarting the dialogue, and of course Israel does not interfere in election processes in other places," the official said.Talks frozen
A spokesman for Abbas told the official PA news agency WAFA that Lieberman's statements "do not contribute anything to creating an environment of peace" and he urged Netanyahu to denounce them.
Another Palestinian official, Azzam al-Ahmad, strongly condemned the remarks.
"We say it very clearly that if Israel is serious about the peace process, it should get rid of such personalities whose only concern is to talk like the Mafia," the Fatah official said.
"Neither Lieberman nor the Israeli side has a right to intervene in internal Palestinian affairs."
US-hosted peace talks between Israel and the Palestinians collapsed shortly after they restarted in 2010, in a dispute over Israeli settlement-building in the occupied West Bank.
Abbas has said negotiations could resume only if Israel halted settlement construction. Netanyahu, who refused in 2010 to extend a 10-month moratorium on housing starts in the occupied West Bank, has dismissed preconditions.
"In a calculated manner, Mr Abbas is focusing his dialogue with the international community on the subject of settlements," wrote Lieberman, who himself lives in a settlement.
"Unfortunately, the international community tends to accept this discourse, lock, stock and barrel, without criticism or a nuanced approach," he added.
Palestinians fear settlements, built on territory Israel captured in a 1967 war and which they seek for a future state, will deny them a viable country in any peace deal.
The World Court and the European Union regard settlements as illegal under international law. Israel disputes this and cites historical and Biblical links to the West Bank, an area it calls Judea and Samaria.Ma'an staff in Bethlehem contributed to this report.
JERUSALEM (Reuters) -- Israeli Prime Minister Benjamin Netanyahu rebuked his far-right foreign minister, Avigdor Lieberman, on Wednesday for suggesting Palestinians should vote out their president to help revive peace efforts.