It also increases the number of MPs to be elected in the northern autonomous Kurdish region after many Kurds threatened to boycott the polls if the three provinces they control were not allocated more seats.
Osama al-Nujeifi, a Sunni parliamentarian, said the amendment would transfer seats from northern provinces where Sunnis have a strong presence to the Kurdish-run north.
"It is a way to steal seats from Mosul and Salahuddin provinces and give them to Kurdistan provinces in an illegitimate way," he said.
Shia-dominated provinces will also broadly have fewer seats under the new law but are likely to retain a substantial majority in parliament.
Salim Abdullah, a spokesman for the Accordance Front, the biggest Sunni bloc in the parliament, said: "What has happened today represents a setback to the policy of political accordance that the parliament has adopted."
The failure to tackle the issues raised by Hashemi has raised concerns that the elections could be delayed beyond the January 31 deadline set by the constitution.
"I must give you a very important notice: his excellency [Hashemi] will veto this again, but this will be considered his second veto," Baha al-Araji, the head of parliament's legal committee, said.
If a second veto is used, MPs can overturn it with a 60 per cent majority in parliament. An alliance of Shia and Kurdish MPs could pass that threshold with around 30 votes to spare in the 275-seat assembly.
The country's presidential council, which composes of Jalal Talabani, the Iraqi president who is of Kurdish descent, and two vice presidents - Adel Abdel Mehdi, a Shia, and Hashemi have 15 days to pass judgement the new text.
Only one official from the three-member council would need to veto the bill for it to be sent back to parliament.
Faraj al-Haidari, the chief of the election commission, said that the body would wait for the council's response before "deciding future moves" for organising the vote.
"I think that it is very difficult to hold the elections in January. Most probably, it might be moved to February," he said.
The election could also be delayed by a parliamentary recess for the Muslim Eid al-Adha festival that means MPs would not be able to vote to ignore any veto until December 8.
In Washington, Hillary Clinton, the US secretary of state, conceded that the election date "might slip", but she expressed confidence that the voting eventually take place.
The elections will be Iraq's second since Saddam Hussein was toppled in a US-led invasion in 2003.