Aljazeera’s correspondent in Jerusalem said Sharon had offered to transfer security control in Qalqaliya and Bethlehem within two weeks provided the Palestinian leadership controls the resistance factions.
In addition, Sharon offered to allow entry of 16,000 Palestinian workers and ease the movement of Palestinians at crossings.
But, talking after the two-hour meeting at Sharon's residence in Jerusalem, Palestinian Prime Minister Ahmed Qureia said: It was a difficult meeting and it did not meet our expectations.
"There were no positive answers to the issues we raised," Qureia said, mentioning the reopening of Gaza's airport, further releases of Palestinian prisoners in Israeli jails and Jewish settlement expansion in the West Bank.
In a gesture to Abbas, Sharon offered to pull back Israeli forces from Bethlehem and Qalqilya in the West Bank within two weeks, but conditioned the move on a credible Palestinian plan to rein in anti-Israel fighters, the Israeli leader's spokesman said.
"We are still taking casualties," Sharon complained to Abbas. The remarks seemed to set the tone for the session, which lasted a little more than two hours.
The meeting was held a day after Palestinian fighters killed a Jewish settler in the West Bank and Israeli soldiers shot dead a Palestinian civilian in a restricted area in the Gaza Strip, incidents that further frayed a four-month-old ceasefire.
In a sign of impatience with Abbas over his refusal to meet Israeli demands to disarm Palestinian resistance fighters, Israeli forces detained dozens of Islamic Jihad members in the biggest West Bank raid since he and Sharon declared the truce at a February summit in Egypt.
The Jerusalem summit, the first between an Israeli prime minister and a Palestinian president in the holy city at the heart of the Middle East conflict, brought both men together before Israel's planned withdrawal from Gaza in mid-August.
"It was a difficult meeting and it did not meet our expectations. There were no positive answers to the issues we raised"
Palestinian Prime Minister
Despite US pressure to coordinate the pullout, Sharon and Abbas gave no outward sign of cooperation. They did not appear together in public during the summit, nor hold a joint news conference afterwards.
The Israeli leader has been seeking stronger steps from Abbas to prevent Palestinian fighters from disrupting the pullout and filling a potential power vacuum afterwards.
"The disengagement plan will go according to plan and schedule under two possible scenarios, either coordinated with the Palestinians - they take the necessary steps - or unilaterally, and we will take all the necessary steps," Sharon spokesman Raanan Gissin told CNN after the meeting.
Abbas says he needs to show Palestinians clear Israeli commitments to relieve burdens of occupation, such as roadblocks and sealed borders, in return for efforts to ensure the pullout is not carried out under fire.
Both sides have accused each
other of violating the ceasefire
He also wants Israel to free more of the 8000 Palestinians in its jails, including long-serving inmates. The issue, raised at the summit, is highly emotive for Palestinians.
"We are willing to consider that but there is no way that this thing could pass in the Knesset or in the government or in the Israeli public when terrorism continues," Gissin said.
Israel has freed 900 prisoners since the truce was declared.
Islamic Jihad arrests
Washington is counting on Israel's evacuation of all 21 settlements in Gaza and four of 120 in the West Bank to kick-start a US-backed international road map peace plan.
Sharon, however, reaffirmed at talks in Jerusalem on Sunday with US Secretary of State Condoleezza Rice that he will not enter into talks on Palestinian statehood until Abbas disarms and dismantles resistance groups.
Abbas, whose January election to succeed the late Yasser Arafat revived peace hopes, says he wants to co-opt fighters into Palestinian security forces and their groups into mainstream politics rather than risk confrontation and possible civil war.
"We are willing to consider that (the freeing of Palestinian prisoners) but there is no way that this thing could pass in the Knesset or in the government or in the Israeli public when terrorism continues"
Ariel Sharon's spokesman
Just hours before the summit, Israeli soldiers took 52 Islamic Jihad members into custody in the West Bank.
Islamic Jihad said attacks it has carried out against Israelis since the ceasefire were in response to recent Israeli raids in the West Bank against several of its men.