The Likud said in response that the Kadima chairwoman's remarks reflect stress. "This is a ridiculous spin," the party said in a statement.
In closed forums over the weekend, following US President Barack Obama's inauguration and Mitchell's appointment as Mideast envoy, Livni said, "Mitchell's mission is a positive thing under a government which will continue the current diplomatic policy.
"When Israel supports a solution of two states for two people, the pressure won't be on Israel. If we have a government headed by myself which will advance this policy, the pressure will be exerted on Iran and its satellite countries and we'll be able to recruit the US to our war on terror.
"If we have an extreme right-wing government, which will reject this principle, the pressure will be directed at Israel."
According to Livni, "Obama's policy could be an opportunity for Israel. He wants to be involved and solve the conflict. His pressure will be directed at those who refuse this process, and Israel must choose whether it's on the side advancing a peace process or on the side of those refusing it, otherwise there will be an inevitable rift with the United States here."
'Netanyahu knows US better than anyone'The Likud responded to the remarks by saying, "Livni is stressed because she knows she will be losing the elections in 16 days, so she's shooting at all directions and spreading a ridiculous spin, reflecting Livni and Kadima's great distress.
"(Likud Chairman Benjamin) Netanyahu knows the United States better than any other leader, will manage the relationship well and will know how to maintain the State of Israel's vital interests in the international arena."
During his visit, Mitchell is expected to visit Israel and the Palestinian Authority. He will meet with the prime minister, foreign minister, and other senior officials in Jerusalem, and is also expected to meet with the Palestinian president and prime minister.
Upon his appointment as Mideast envoy, Mitchell clarified that peace in the Middle East was a security-related interest of the US and that there was no such thing as an unsolvable conflict.
Yesha Council Chairman Danny Dayan told Ynet on Saturday evening that Mitchell's appointment was "very disturbing".
"Soon we will need to get Obama's request to have children," Dayan said, alluding to Mitchell's previously voiced objection to allowing natural growth in West Bank settlements.
Meanwhile, Saudi Arabia is also increasing its pressure on the US to advance peace. A member of the Saudi royal family warned Obama on Friday the Middle East peace process and US-Saudi ties were at risk unless Washington changed tack on the Israeli-Palestinian conflict.
Israel had come close to "killing the prospect of peace" with its offensive in Gaza, Prince Turki al-Faisal wrote in an article published on the Financial Times' website.
"Unless the new US administration takes forceful steps to prevent any further suffering and slaughter of Palestinians, the peace process, the US-Saudi relationship and the stability of the region are at risk," said Turki, a former Saudi intelligence chief and former ambassador to the United States and Britain.
The Bush administration had also contributed to the "slaughter of innocents" in Gaza, said Turki, who currently holds no official government position in the world's top crude oil exporter.
"If the US wants to continue playing a leadership role in the Middle East and keep its strategic alliances intact -- especially its 'special relationship' with Saudi Arabia - it will have to drastically revise its policies vis-a-vis Israel and Palestine," Turki wrote.
Amnon Meranda and Reuters contributed to this report