The amended law says that all future parliamentary candidates will be chosen according to party lists.
The changes put an end to candidates being chosen in single constituencies.
The new draft makes it easier for candidates from Fatah to run in the Gaza Strip, which has been under the control of Hamas since its fighters pushed out Fatah forces in June.
Fawzi Barhoum, a spokesman for Hamas, said the decision to amend the electoral law is "illegal", and dismissed Abbas' call for fresh elections.
"Early parliamentary elections are rejected ... and any amendment to the law is also rejected," he said.
"Hamas objects to this policy of monopolising decision making and will not deal with its outcome."
After Hamas took over the Gaza Strip, Abbas sacked the Hamas-led unity cabinet and installed a new cabinet.
Hamas has refused to recognise the replacement administration, saying that the coalition cabinet led by Ismail Haniya, the prime minister sacked by Abbas, is the sole legitimate government of the Palestinians.
Barhoum said only the Hamas-controlled parliament has the authority to change electoral law, but Abbas says he now holds such authority since parliament is no longer effective.
Hamas won the last parliamentary elections in January 2006, handing a surprise defeat to Fatah.