Abbas, addressing a special parliamentary session on Thursday aimed at securing more powers, urged the body to throw more support behind him or send him home.
The prime minister has been embroiled in an increasingly bitter dispute with veteran Palestinian President Yasir Arafat, mainly centred over control of the security apparatus.
Abbas admitted to problems between his government and Arafat, calling for “the healing of problems”.
“ I do not deny the existence of problems in our administrative relations between the government and the presidency," Abbas told a special session of parliament. "This problem needs to be fundamentally corrected.”
Arafat appointed the premier on 30 April under intense US pressure.
Abbas was speaking to the 85-member Palestinian Legislative Council in the occupied West Bank city of Ram Allah, where Arafat has been under siege in his headquarters.
On the peace process, Abbas called on the United States to end its boycott of Arafat.
Abbas, hailing ties with Washington, said Arafat was the "constitution and legitimate president” of the Palestinian people.
Washington has sidelined Arafat in any peace negotiations, preferring instead to deal with Abbas.
"Road map" issues
The United States is not putting enough pressure on Israel to implement the US-backed “road map” aimed at ending the Palestinian-Israeli conflict, he said.
The power struggle between Abbas and Arafat is centred on the premier’s demand, backed by Washington, for control over the security forces.
He also accused Israel for the end of a ceasefire declared by Palestinian resistance groups aimed at ending anti-occupation attacks, saying the Jewish state had resumed its policy of targeted killings after being embarrassed by US criticism for a wall construction separating the West Bank from Israel.
Israel restarted its assassination policy last month, killing 11 Hamas activists in helicopter attacks, in less than a month, and pledging to make all resistance fighters legitimate targets, a stance condemned by Palestinians.
Abbas said Israel's killings of Hamas activists ended the truce called for by the resistance groups. "It destroyed the 'hudna' (ceasefire) through a political decision."
The premier said he would not crack down on Palestinian activists- a key Israeli and US demand.
He urged the international “quartet” to work harder to salvage the “road map”. The blueprint was co-sponsored by the United States, United Nations, Russia and the European Union in June, but has not been able to move beyond its first stage.
Following the meeting, a group of 18 Palestinian members of parliament filed an application for a vote of confidence to be held against Abbas, said Parliament speaker Ahmad Qurayaa.
Some of the legislators include independents and members of Arafat's Fatah movement.
Abbas sought to defend his record
over the last four months
Abbas also reappointed Saib Urakat as the Palestinians' chief negotiator. Urakat handed in his resignation to Abbas two weeks after the establishment of a new Palestinian government in April.
He did not give a reason for his resignation, but political sources said Urakat was reacting to his exclusion from talks between Abbas and Israeli Prime Minister Ariel Sharon.
The power struggle between Abbas and Arafat is centred on the premier’s demand, backed by Washington, for control over the security forces. It is seen as crucial for reining in the resistance against Israel.
Arafat has appointed former rival and strongman Jibril al-Rajub as security adviser.
Al-Rajub is perceived as close to Arafat and one of the few people strong enough to face off the Palestinian Internal Security Minister Muhammad Dahlan.
Arafat’s Fatah Shabiba (Youth) Organisation staged protests against Abbas’s government during the parliament meeting.
Shabiba issued a statement condemning the prime minister and the internal security ministry headed by Dahlan, comparing Abbas’s government to the US-appointed Iraqi Governing Council.
In Washington US Secretary of State, Colin Powell, said forces that currently receive orders from Arafat should be placed under Abbas’s responsibility.