"I will tell him [Mitchell] clearly: there are many conflicts in the world that haven't reached a comprehensive solution and people have learned to live with this," he said, citing continuing land disputes in Cyprus, Nagorno-Karabakh and the Falkland Islands.
But Barak told Mitchell that "the time had come to move determinately forward" and that comprehensive peace in the Middle East was not a "zero-sum game" but a "win-win" situation for both Israel and the Palestinians.
Ian Kelly, the US state department spokesman, responded to Lieberman's comments by saying: "I'm not going to put a qualifier on that - the main thing is that [both sides] have to agree to sit down."
Aaron David Miller, a former US state department official and an adviser to six US secretaries of state, told Al Jazeera that Lieberman was "addressing the requirements of his constituency and his own personal view".
Mitchell is expected to meet Binyamin Netanyahu, the Israeli prime minister, and Mahmoud Abbas, the Palestinian president, on Friday.
But analysts say there is little momentum for progress towards formal talks between Israel and the Palestinians despite Barack Obama, the US president, saying he hoped for significant development by mid-October.
"The credibility of the Palestinian president, as it relates to the negotiations, among the people and even within [Abbas's] Fatah movement, has today become very shaky"
Miller said that the domestic challenges facing the Israeli and Palestinian leaders, as well as a range of problems facing Obama, did not augur well for progress towards formal peace negotiations.
"Given courageous and determined Palestinian and Israeli leaders, and a US president who is prepared to be smart, tough and fair, the odds of reaching an agreement migh not be so bad - but the reality is that that is not what we have right now," he said.
"We have two leaders - Benyamin Netanyahu and Mahmoud Abbas - who are prisoners of their politics, not masters of their constituencies.
"We have a US president who has all the right instincts, who is quite persuasive and compelling, but I am not entirely persuaded that this issue, among all the others such as Iran, Afghanistan, Iraq and US healthcare is going to be the kind of priority that is going to allow him to be tough, smart and fair [on the Israel-Palestinians issue]."
Mitchell's visit comes as Palestinians carried out a sit-in at al-Aqsa mosque in protest over the presence of right-wing Israeli's on the site. Israel had sent thousands of police and soldiers into occupied East Jerusalem following clashes between Palestinians and Israeli settler activists around the al-Aqsa mosque compound.
On his last visit to the region, Mitchell got Netanyahu and Abbas to agree to a three-way summit with Obama on the sidelines of the UN General Assembly.
But US pressure has had undesired effects, according to Palestian political analysts. They say the summit in September weakened Abbas and his ability to make concessions.
Abbas had pledged not to meet Netanyahu until Israel stopped illegal settlement building.
"The credibility of the Palestinian president, as it relates to the negotiations, among the people and even within [Abbas's] Fatah movement, has today become very shaky," Samih Shabib, a Fatah official, said.
Pressure on Abbas
The Palestinian president has also come under widespread Arab criticism for apparently submitting to US and Israeli pressure by not pressing for a vote at the UN on a report which accused Israel of committing war crimes during the Gaza war.
Palestinians have also been critical of the US for not pushing Israel to accept the freeze on building of Jewish settlements in the occupied West Bank.
Ziad Abu Zayyad, a former Palestinian legislator, said: "I don't expect any change. The Palestinians are the weakest party in the talks and the Obama administration during the past week has made it clear it is done putting pressure on Israel and is now going to apply the pressure on the Palestinians."
Netanyahu, on the other hand, has apparently been emboldened by his success in parrying Obama's demands for a settlement freeze.
"Mitchell has a lot of problems because we now know that you can say no to a US president and still survive," Eytan Gilboa, an expert on Israel-US relations from the right-leaning Bar Ilan University, said.
"There is a direct connection to the strength of the president and the strength of his personal envoy. Mitchell had a lot more power three months ago."