Thursday's meeting in London was the first between the two sides since the collapse last month of the latest round of talks, and came after both held separate talks with US Secretary of State John Kerry.
But Prime Minister Benjamin Netanyahu's office and ministers quickly moved to distance themselves from the Livni-Abbas meeting, insisting it was private and did not signal any official intention to resume talks with the Palestinians.
Israel pulled out of the talks in mid-April, saying it would not negotiate with any Palestinian government supported by Hamas after the leadership in the West Bank signed a unity deal with the rival Islamist rulers of Gaza, who are committed to the destruction of the Jewish state.
"Prime Minister Netanyahu made clear to Minister Livni even before her meeting with Abu Mazen (Abbas) that she would be representing only herself and not the government of Israel," the official said.
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"Netanyahu made it clear to Minister Livni that Israel's position, as decided unanimously by the (security) cabinet, was that the Israeli government will not conduct negotiations with a Palestinian government supported by Hamas, a terror organisation whose declared intention is the destruction of Israel."
"I don't know of any civilised Western country where a minister would meet, on his own initiative, the head of an authority or state in a period of crisis and tension," he said at the start of the cabinet meeting, in remarks broadcast on army radio.