Senior PPP leaders have alleged there were "political motives" behind the assassination and claimed that some elements in the opposition PML-N might have been behind the crime.
PPP leaders in Punjab were not convinced by Taseer`s killer`s confession that the assassination was an "act of faith".
Some of them believe the murder was part of a plot to pit the PPP against religious forces.
However, President Asif Ali Zardari has said it is "yet to be established" whether Governor Taseers assassination was a "conspiracy against the system" even as leaders of the ruling Pakistan People`s Party held the PML-N-led government in Punjab responsible for the murder.
"It is yet to be established whether the assassination was a conspiracy against the system and the country behind the facade of religion," Zardari told PPP lawmakers during a meeting in Karachi, where he has been camping for the past few days.
Noting that investigations were underway into the murder, Zardari expressed the hope that "soon the motives behind the macabre crime and the perpetrators and planners will be exposed and punished".
Taseer`s assassination was a "great tragedy and a huge loss to the PPP", the President said.
He vowed to convert "this loss into strength for the party and the people".
Taseer was gunned down in Islamabad on Tuesday by police guard Malik Qadri, who said he was angered by the Governor`s criticism of the blasphemy law.
Investigators are trying to determine whether Qadri acted on his own or others were involved in the killing.
The PPP is refusing to accept that Taseer was killed on religious grounds and party spokesperson Fauzia Wahab said there were "political motives" behind the murder.
The killing appeared to be an "organised act" and the Punjab administration was "equally responsible" for the crime, she said.
Federal Law Minister Babar Awan, a close aide of PPP chief and President Zardari, too described the assassination as a political murder and told a meeting of party lawmakers on Wednesday that the way the Governor was eliminated raised many questions.
"Mr Taseer was made to leave his home for assassins," Awan said, adding "some forces" were involved in such acts to weaken the country.
The meeting adopted a resolution demanding that the Punjab government should "unearth the conspiracy behind the murder". They rejected a perception that religion had anything to do with the crime.