"He who makes such conditions does not want peace," a senior Israeli official told AFP on condition of anonymity.
Abbas listed his demands during a meeting with Israeli journalists at his headquarters in the West Bank just a week before a nine-month target for a peace deal.
His comments came as US envoy Martin Indyk went into a new meeting with Israeli and Palestinian negotiators in a bid to save the US-sponsored talks from collapse.
"There must be a total freeze of settlements," by Israel in the occupied West Bank including annexed east Jerusalem, Abbas said.
"The borders between Israel and the state of Palestine must also be defined within a month, two or three," if the talks are to be extended, he said.
The Palestinians have long viewed Israeli settlement construction as a major obstacle to peace talks, arguing that Israel is actively building on land that should be part of their future state.
But the senior Israeli official told AFP that settlement building in Jerusalem would not be frozen and that Israel had never agreed to discuss the border issue separately from other core issues.
These include Palestinians refugees, the fate of Jerusalem, which both sides claim as a capital, security and mutual recognition.
"It is impossible to define borders before an agreement on the other issues," the Israeli official said.
"This has been clearly explained to the Palestinians. Never has Israel committed not to carry out expulsions," he said.
