A senior official in the Prime Minister's Office told Ynet on Friday that "the opportunity for a dialogue with the Palestinians lies with Abu Mazen (Palestinian President Mahmoud Abbas) and the presidency."
Lieberman, however, called on the government to immediately sever its ties with the Palestinian president.
"Abu Mazen has consented to Hamas' desire to destroy us," he said. "We must therefore discontinue our relations with him. I am familiar with the prime minister's stand on this and his views are different from mine," the minister told Ynet.
The senior source at the Prime Minister's Office said that the prime minister believed all doors must not be closed, and that the channel of dialogue with the Palestinians must be left open.
"There are many interests that should be implemented as far as Israel is concerned, but the diplomatic dialogue, in the current situation, will be limited. It's obvious that in such a situation it will be difficult to sign any diplomatic agreement, and definitely not a permanent agreement," he said.
However, the official explained, "There is still a series of issues to be discussed. We plan to continue holding discussions with Abu Mazen on the ease of restrictions on the Palestinian population and on security issues related to the war on terror.
"We plan to continue demanding that the Qassam fire stops, that the smuggling of weapons to Gaza is halted, and that the international community pressures the Hamas government. And of course we cannot forget the release of (kidnapped soldier) Gilad Shalit."
Aides to Olmert said Friday that "it is not true that Abbas has no control over this government. The fact that Hamas went to a unity government with him proves that he does not lack influence. He apparently has something to give.
"What we have to do is ensure that the things he has to give are working in our favor, and in the favor of both people. It would be a mistake to sever relations with him at this time."
'Want peace? Recognize Quartet conditions'
Meanwhile, diplomatic sources in Jerusalem responded to the statement made by Palestinian information minister-designate, Dr Mustafa Barghouti, that if Israel wants peace, it would have to recognize the new Palestinian government.
"If the Palestinians want peace, they must recognize the international community's conditions, this is a basic and necessary condition," said the source.
"No word game can get the out of their commitment to uphold the international community's three preconditions," he added.
At the same time, new United Nations Secretary-General Ban Ki-moon will also be visiting Israel for the first time since his election. The officials plan to hold a round of talks with Israeli and Palestinian leaders in order to open dialogue between the parties.