The meeting was held after many months of preparation.
"We plan to continue to meet in order to implement the joint understandings and the diplomatic agenda we wish to promote, "Olmert added during the cabinet meeting.
The prime minister told the ministers that the meeting was the outcome of many efforts, which were exerted for a long time.
"From the first day I went into office I expressed my desire to meet Abu Mazen (Abbas), but due to pressures, internal problems and other issues, the meeting did not take place.
"Yesterday, after I expressed my desire more than once to hold the meeting without any preconditions, the PA chairman accepted and was a guest at my home. We discussed a series of issues over dinner and reached agreements," Olmert said.
Olmert also briefed the ministers that in his meeting with Abbas he agreed to ease a series of restrictions, including the transfer of USD 100 million to the Palestinian Authority for humanitarian purposes.
"We decided to help the residents, who are suffering from the failures of their government, which is not part of the international community," he explained.
He stressed that the funds would be transferred through a mechanism, which will ensure that they do not reach the Hamas-led government.
Olmert also reported of an ease of restrictions in crossing and of the establishment of a committee to discuss the prisoner release issue.
Ministers welcome summit
Deputy Prime Minister and Industry, Trade and Labor Minister Eliyahu Yishai welcomed the summit.
"I hope the meeting will bring Gilad Shalit back home, even if there is a certain price we have to pay. We have to exert every effort, including a meeting with Abu Mazen," he said.
Referring to the Qassam fire, which continued Sunday morning, Yishai said that it is clear that the organizations have no plan to honor the ceasefire.
"We have to operate specifically against anyone launching rockets. They cannot continue making fun of the State of Israel."
Vice Premier Shimon Peres also welcomed the leaders' meeting, saying that "I am certain it will be continued in diplomatic activities.
Foreign Minister Tzipi Livni concluded, "This is an important meeting to ease the daily life of the Palestinians, but simultaneously, we must also promote a significant diplomatic initiative with Abu Mazen and the moderates in the PA.
"The Palestinians have two choices: The extreme Hamas option or a moderate option, which included a diplomatic horizon."
Defense Minister Amir Peretz expressed his support of the gesture of releasing Palestinians prisoners in honor of Id al-Adha and Christmas holidays, but expressed his doubts over the restraint policy following the Qassams.
He presented the evaluation of defense sources, according to which there is no guarantee that this policy is in fact in favor of the moderates in the PA, and said that it seems it is actually helping those who claim responsibility for firing rockets.
"We can operate against the Qassam launchers by setting parameters such as firing at open areas, in order to minimize the harm caused to innocents," he said.
During the cabinet meeting, Olmert also addressed the other "hot" issue on the agenda – the sanctions imposed on Iran by the United Nations Security Council.
The prime minister welcomed the sanctions, saying that "this is an important decision of the international community. It provides many options to block the Iranian government's nuclear option."