The decisions were adopted by consensus. Mahmoud Zahar, a Hamas leader, said the group would try to derail elections.
"The Palestinian people - and Hamas is a part of the people - will not allow early elections to create results that America approves of," he said in Gaza City.
Meanwhile, Hamas denied an Israel accusation that it had significantly stepped up weapons smuggling since taking over Gaza last month.
A senior Israeli security official said Hamas had brought 20 tonnes of explosives into Gaza and was trying to import longer-range rockets.
Fawzi Barhoum, a Hamas spokesman, said: "This is not true. They want to use this as a pretext to tighten the siege on Gaza."
Abbas and Hamas have been wrangling over political legitimacy since the Gaza takeover last month. Abbas, separately elected in 2005, fired the unity government with Hamas and installed a West Bank-based emergency cabinet.
Hamas has denounced the measures as unconstitutional.
It remains unclear whether Abbas is serious about a new vote or simply trying to press Hamas to reverse its Gaza takeover.
Some participants in Thursday's Central Council meeting said they believe Abbas is simply trying to force Hamas to reverse the takeover, and that in such a case he would quickly call off elections.
"Our call for early elections is another means of pressure on Hamas to retract," said Ahmed Majdalani, a member of a small PLO faction.
The risks of holding elections are high. Abbas aides have said he would run for president again, even though polls indicate his popularity is low and he would be neck-and-neck with Hamas's most popular politician, Ismail Haniya, who was deposed as prime minister by Abbas last month.
Even if voting goes ahead in the West Bank, a Fatah stronghold, there is no guarantee Abbas or his party would win.
Fatah was ousted in 2006 because of widespread voter anger over official corruption, and the party has failed to reform.