Abdul-Karim, a member of the Democratic Front for the Liberation of Palestine, said the president had the right to amend local elections' law.
But, "in such case, the president will be responsible before the Palestinian Legislative Council and public opinion. Since the election law has not been amended, the decision to postpone elections is illegal," he said.
The elections shouldn't necessarily be dependent on national reconciliation because it is evident that a deal between Hamas and Fatah is far from being implemented, the DFLP official added.
People should also not be deprived of their democratic rights under the pretext of a disagreement, he added.
The Palestinian Democratic Union, Fida, has also voiced disagreement over the postponement of elections, saying the decision violates the election law of 2005 and also ignores a previous 2010 decision by the Palestinian High Court of Justice which annulled a decision to postpone elections that year.
Fida called on President Mahmoud Abbas to retract his decree and urged all Palestinian factions, political parties and civil society organizations to protest the decision and organize popular protests.
"It is evident the decision was based on a bilateral agreement between Fatah and Hamas, which indicates the two movements are still monopolizing decision-making and ignoring Palestinian law and consensus,” a statement from Fida said.
Abbas issued a decree on Monday postponing local West Bank elections "until appropriate circumstances" exist.
The postponement will provide the "appropriate environment" for efforts to end "division and reaching reconciliation and national unity," the decree said.
Local elections were last postponed in July 2011 to give more time to a reconciliation agreement between rival parties Hamas -- which rules the Gaza Strip and refuses elections until the electoral commission is reformed -- and Fatah in the West Bank, signed in May.
Rescheduled elections were planned for the West Bank only, with officials saying Hamas was blocking efforts to prepare for the October vote in Gaza.
The last time the Palestinians went to the polls was for parliamentary elections in 2006, which Hamas won by a landslide.
New parliamentary and presidential elections had been due to be held in January 2010 but the Palestinian Authority abandoned efforts to hold a vote after Hamas refused to organize one in Gaza.
Maan News Agency