A second veto would send amended law back to parliament for a new round of voting.
An alliance of Shia and Kurdish parliamentarians could theoretically pass that threshold with around 30 votes to spare in the 275-seat assembly.
But the debate over representation has lead to fears of further sectarian division in Iraq ahead of the polls.
Al Jazeera’s Zeina Khodr, reporting from northern Iraq, said that Sunni politicians felt an agreement was unlikely to be reached, because it would require the Kurds to give up some of their seats in parliament.
“A Sunni MP said there’s a lack of political will on the parts of the Kurds, who hold the key to a compromise.
“They were given extra seats at the expense of Sunni governorates [when the proposed law was last amended] … Kurds will have to give up those seats for a compromise to be reached.”
Tribal elders in Tikrit, a mainly Sunni town about 140km northwest of Baghdad, have threatened to call for a boycott of the elections.
“That would mean yet again another community will be marginalised out of the political process. The consequences could be a security vacuum,” our correspondent warned.
‘No population data’
Ala al-Talabani, a Kurdish member of parliament, told Al Jazeera that poor population statistics in Iraq was complicating the allotment of seats in parliament.
Iraq’s constitution stipulates that laws passed by the parliament must be approved unanimously by the presidential council.
The council currently consists of Jalal al-Talbani, the president, Tariq al-Hashimi, vice-president, and Adil Abd al-Mahdi, also a vice-president.
If a presidential council member vetoes a law, it must go back to parliament for a vote on whether to accept the veto and change the law accordingly, or refuse the veto and send back the law unaltered to the council.
The presidential council has the right to veto each law twice.
If the council vetoes a law on two occasions, the law is kicked back to the parliament again. In this case, the law must be approved by 60 per cent of the parliament’s members – otherwise the parliament must change the law to win the approval of the presidential council.
She said high growth was recorded in some major cities while statistics did not show any growth at all in cities like Sulaimaniya in the Kurdish region.
“The problem is that in Iraq, we don’t have fixed data of the population in each province … That’s why the discussion is about how the electoral commission is going to calculate the seats for each province.”
Under Saddam Hussein, the late Iraqi leader who was toppled in a US-led invasion in 2003, Iraq’s minority Sunnis held power.
But following the invasion, the majority Shia took command of the nation’s political leadership and security forces.
The political back-and-forth has also held up the planning for Iraq’s elections, scheduled for January 16.
In principle, Iraq’s constitution requires that parliamentary elections be held by the end of January, but many analysts say that is unlikely to happen.
The United Nations has proposed February 27 as the most “feasible” date for the poll.
Al-Hashemi has warned that he may again use his veto, but said on Saturday he thought progress was being made towards an agreement.
“There are optimistic signs and I hope the remaining simple points of dispute will be resolved by the political groups,” he said on state-run al-Iraqiya television.
Al-Hashemi also added a warning to some of the Shia blocs that have objected to the possible concessions to Sunnis.
“I hope the hard line adopted by some people in parliament will not compel me to use the veto again,” he said, without naming specific legislators.
Parliament met on Saturday to vote on a new electoral law, but not enough legislators turned up for the meeting to be quorate and a decision was delayed until Sunday.