Abbas, who belongs to Fatah, has the authority to dismiss the Hamas government, but has been reluctant to do so because any new cabinet would need to be approved by the parliament, which is dominated by Hamas.
A Hamas spokesman on Saturday termed the PLO leaders' call as an attempt to overturn the Palestinian people's democratic choice.
"We warn that such decisions will lead to more division that will heat up the atmosphere," Ismail Radwan said.
The president also has the option to call a referendum asking if new elections should be held, but this could also be problematic as Fatah have been shown to be struggling in recent opinion polls.
"The trend within this committee is to recommend early elections"
Azzam al-Ahmed, head of the Fatah bloc in parliament
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Azzam al-Ahmed, the head of the Fatah bloc in parliament and a member of a committee formed on Friday to help decide the next steps, has recommended that Abbas call early elections.
"The trend within this committee is to recommend early elections," he told AP news agency. "This choice, the early election, will be much better than the current situation, even if Fatah lost both the presidential and parliament elections."
The committee will meet on Saturday to discuss the options and Abbas plans to address the Palestinian people "very soon" to discuss his next move, Saeb Erekat, an aide to the president, said.
The PLO has agreed that the talks would not resume any time soon unless Hamas agrees to Abbas' demands.
"The talks must be resumed when the conditions are appropriate ... specifically the acceptance of [Abbas's] political programme," the body said.
Hamas on Friday criticised Abbas for saying the talks were over and 6,000 people attended a rally in Gaza calling for a resumption of negotiations.