Abbas urged Hamas to join Fatah in a unity coalition in order to get the sanctions lifted. But the talks ended in deadlock over the division of cabinet portfolios and the issue of recognising Israel.
Talks on forming a unity government broke down last month.
Ismail Haniya, the Palestinian prime minister, rejected Abbas's plan to hold early elections, saying it would accentuate "crisis and tensions".
"I think that the invitation to carry out the elections in this way is disrespectful to the Palestinian people," Haniya said in an interview with Iranian television on Saturday.
"I believe that this will increase the crisis and the tensions and will have a negative impact," said the head of the Hamas-led government, who is visiting Iran as part of his first foreign trip as prime minister.
Khalil al-Hiyya, the chief of the Hamas bloc of lawmakers, told AFP in Gaza City earlier that "the goal of this decision is to kick Hamas out of the Palestinian political scene."
"This decision is not in the national interest and will only make the situation more tense."
"We had an intense discussion on various options, and from what we heard, he is leaning toward going back to the people with a call for early presidential and legislative elections," Saeb Erekat, a senior Palestinian aide, said.
"This is political blackmail at its worst"
Docinfujairah, London, United Kingdom
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Participants in Saturday's meeting said Abbas has not set a deadline for holding the new election.
But an official close to Abbas said the election would probably be held in four or five months. The official spoke to the Associated Press on condition of anonymity.
Calling a new election would be risky for Abbas as he would be putting his own job on the line and there are no guarantees that Fatah would improve its standing in a new vote.
The movement, which dominated Palestinian politics for four decades, remains divided and tarnished by corruption.