The meeting, on the sidelines of a World Economic Forum conference in the Red Sea resort of Sharm El-Sheikh, came amid Israeli raids on the Palestinian territories and a surge in violence between rival Palestinian factions in the Gaza Strip.
Israel officials vowed they would act to prevent a humanitarian crisis in the Palestinian territories, which are in the grip of financial crisis after Israel and western governments cut aid to the Hamas-led government.
"It is the Israeli government policy not to punish the Palestinian people for their vote and to help the Palestinian people in any economic and humanitarian way that we could," Israeli Foreign Minister Tzipi Livni said after the talks.
"Israel is not against the Palestinian people and will do all it can to prevent a humanitarian crisis," added Deputy Prime Minister Shimon Peres, who was also at the meeting.
"We want to ensure that there is aid to the people and not to the terrorists."
Israel has boycotted Hamas since it took office at the head of the Palestinian government in March, as the Islamist movement still refuses to recognise the Jewish state's right to exist nor renounce violence.
Sunday's meeting came as new Israeli Prime Minister Ehud Olmert headed to Washington where he will meet US leader George W Bush on Tuesday in a summit expected to be followed by an Abbas-Olmert meeting.
Mr Abbas, a moderate from the former ruling Fatah faction, is committed to a negotiated settlement to the Middle East conflict despite the rise of Hamas.
He urged Israel to return to the table of negotiations and "stop saying there is no (real) Palestinian partner" in the peace process.
"Negotiations are within the jurisdiction of the Palestinian Liberation Organisation (PLO), while the (Hamas-led) government does not object to that," he said in debate in which Ms Livni participated.
Ms Livni urged the Palestinian side not to reject "a plan which helps to establish a Palestinian state," in reference to Mr Olmert's plan to fix the final borders of Israel.
But she pointed out that the track of a controversial separation barrier which is being constructed in the West Bank can be changed through negotiations.
Chief Palestinian negotiator Saeb Erakat described the talks as positive and said the two sides had agreed to meet again to lay the groundwork for the possible Abbas-Olmert summit.
"A range of issues were discussed -- political, humanitarian and economic," Mr Erakat said.
"We focused on reviving the partnership for peace. This is one of a series of meetings and we want to make sure there is a good preparation (for the summit)."
As president of the Palestinian Authority and chairman of the Palestine Liberation Organisation, Mr Abbas is responsible for peace negotiations and not the Hamas-led government.
Mr Erakat said the Abbas team had reiterated requests for the Israeli government to release customs duties it traditionally collects on behalf of the Palestinian Authority but which have been frozen since February.
Earlier, the Israeli government announced it had decided to release 50 million shekels (US$11 million) in customs duties to fund the purchase of medical equipment for residents of the West Bank and Gaza.