Moves towards a resumption of Israeli-Palestinian peace talks were mired in rumours, rebuttals, criticism and confusion on Sunday in an indication of the political and diplomatic swamp facing key negotiators and their mediator, the US secretary of state, John Kerry.

In a high-profile dismissal of the embryonic process, Israel's former foreign minister Avigdor Lieberman, wrote on Facebook that there was "no solution to the Israeli-Palestinian conflict, at least not in the coming years, and what's possible and important to do is conflict-management".

Naftali Bennett, economics minister, insisted construction on Jewish settlements in the West Bank and East Jerusalem would continue, regardless of talks.

The comments by two crucial partners in the Israeli coalition are a sign of deep hostility within the government over the agreement for preliminary talks forged by Kerry on Friday.

Meanwhile, a veteran Palestinian negotiator, Yasser Abed Rabbo, denied that a firm decision had been taken to enter talks, saying further clarification was needed on a framework and the Palestinians were still discussing terms with Kerry. According to a Palestinian source, Kerry had written a letter giving a US assurance that the basis of territorial talks would be the pre-1967 border, but it was not clear whether the letter had been delivered.

"If we have well-defined terms of reference and a clear time frame – by which we mean the end of the year – we will go into talks," the source said.

Among the few formal statements of the day, the Israeli prime minister, Binyamin Netanyahu, told cabinet colleagues that resuming the diplomatic process was "a vital strategic interest of the State of Israel, first of all because we want peace". However, any agreement would be put to a referendum of the Israeli public, he added.

The Israeli president, Shimon Peres, congratulated his Palestinian counterpart on "a brave and historic decision to return to negotiations". He added: "Don't listen to the sceptics, you did the right thing."

Among the sceptics were Hamas, the Islamist rulers of Gaza, which described any engagement in talks by the Palestinian leadership as a "betrayal".

There was no firm indication of when preliminary talks in Washington might begin. Kerry said in his statement on Friday that if everything went "as expected" the first meeting would take place "within a week or so".

The main sticking point continues to be the Palestinian demand that the pre-1967 borders form the baseline for territorial negotiations, a guarantee which Israel refuses to give. If Kerry fails to persuade the Palestinians they have firm US backing on the issue, talks may fail to get off the ground. There is also disagreement over the timeframe. Israel is pushing for negotiations to last up to a year, fuelling concern among critics who believe Netanyahu is seeking to give the appearance of diplomatic co-operation while stalling for as long as possible on any outcome.

Any likely agreed time frame will take the Palestinians well beyond the potential flashpoint of the UN general assembly in September, at which they could renew their efforts to become a member state of the global body, a move fiercely opposed by Israel and the United States.

Both sides agreed to refrain from commenting on the ongoing negotiations. "Even people closest to the [Palestinian] leadership know very little," said Ghassan Khatib, former director of communications for the Palestinian Authority. "The thing that bothers me is that it seems that the resumption of negotiations is seen as an objective in itself. But the problem was never the lack of negotiations, direct or indirect. It is the huge gap between Israel's stated position and its practices, and the lack of willingness by the US to put pressure on them."

A Palestinian source said that the publication of EU guidelines on Friday banning funding or grants to Israeli bodies with links to settlements was "decisive" in persuading the Palestinians to take the first steps back to negotiations.

Meanwhile, Tzipi Livni, Israel's justice minister and representative in the Kerry-brokered talks, has urged the EU to designate the Lebanese militant group Hezbollah as a terrorist organisation. Writing in the Guardian, Livni says: "A firm distinction between legitimate, non-violent political parties and terrorist organisations is crucial for the survival of freedom, democracy and moderation. The clear message must be sent to extremists that violence and terrorism is unacceptable and contradictory to our values, and that legitimacy can only be gained through the repudiation of violence."