The comments from Tzipi Livni are being seen as signalling a hardening of Israel's position and a growing rift with the US.
The US and the European Union have suggested they will keep working with Mahmoud Abbas even if a Hamas government takes office in the coming weeks.
The issue of how to deal with Abbas and a Hamas-led government was the main topic at a meeting on Sunday between Livni and David Welch, the US envoy.
Israel Radio reported that Welch presented a policy which said the United States would work directly with Abbas instead of the Hamas-led government.
Without referring to the radio report, Micaela Schweitzer-Bluhm, a US consulate spokeswoman in Jerusalem, said: "We remain fully committed and supportive of him [Abbas]."
Livni disagreed. The moment Abbas appointed Hamas to form the new government, the Palestinian Authority became "illegitimate", she told Israel Army Radio on Monday.
Israel does not want to be in a situation in which it is dealing with Abbas, who is "more moderate, believes in two states ... but is powerless to deliver the goods or enforce it on the Palestinian Authority," Livni said.
"There were elections, the Hamas won. All the attempts to embrace Abu Mazen [Abbas] ... will not help," she said.
Saeb Erikat, the Palestinian chief negotiator, called Livni's remarks "totally unacceptable".
Erikat, a member of Abbas's Fatah movement, which was removed from power in the January elections, said: "The Israelis are trying to undermine the Palestinian people in general because they don't differentiate between one Palestinian and the other."
Ismail Haniya, Hamas's designated prime minister, said in an interview published on Monday that his government would not negotiate with Israel, but said he was ready to discuss day-to-day issues with the Israeli authorities.
He told the Palestinian daily Al-Quds: "Hamas will move to open channels in this direction."
Under Palestinian law, the Palestine Liberation Organisation, headed by Abbas, conducts peace talks with Israel, while the Cabinet is in charge of running the Palestinians' daily affairs.
Haniya: Hamas ready to discuss
day-to-day issues with Israel
Israel and the so-called Quartet of mediators - the United States, the United Nations, the European Union and Russia - are demanding that Hamas should disarm, recognise Israel and accept past Israeli-Palestinian peace agreements. Hamas has so far rejected these conditions.
Should Hamas decide to accept the conditions, it would bring Israel and the Palestinians on track to implement the internationally backed road map peace plan, Livni said.
Livni said: "It is not grandstanding, it is not an attack but a realistic analysis of the situation."
Haniya said on Monday that the group's military wing would only disarm if Israel withdrew from the West Bank, Gaza Strip and east Jerusalem, the areas it captured in the 1967 Middle East War.
On Monday, EU foreign ministers were expected to approve continued aid to the Palestinian caretaker government.
That could include paying $48 million to help run utilities and authorising the World Bank to unblock about $60 million to pay the salaries of Palestinian Authority employees.
By contrast, Israel froze the transfer of $55 million in tax revenues to the Palestinian Authority after a Hamas-dominated parliament was sworn in on 18 February.
In a letter to the Quartet, James Wolfensohn, the international envoy, said the Palestinian Authority is in danger of financial collapse within two weeks, in part because of Israel's decision to freeze the transfers.
Shaul Mofaz, the Israeli defence minister, meanwhile, listed the Jewish settlement blocs in the West Bank he believes should be annexed as Israel draws its final borders.
Most of the settlements he named are relatively close to Israel, but also included Ariel, deep in the West Bank, as well as the Jordan Valley, on the border with Jordan.
"It is not grandstanding, it is not an attack but a realistic analysis of the situation"
Israeli Foreign Minister
The Palestinians want all of the West Bank for their state, and the US has blocked Israel's plans to include Ariel, a settlement of about 17,000, on the "Israeli side" of its West Bank separation barrier, a possible future border.