He had vetoed an earlier election law, agreed by parliament last month, saying it failed to adequately represent Iraqis living abroad, most of whom, like al-Hashemi, are Sunnis.
Al Jazeera's Zeina Khodr, reporting from Irbil, said: "A compromise has been reached to avert a veto by the Iraqi vice president.
"Al-Hashemi's demands have been satisfied. Earlier today he said he wanted to exhaust all efforts because these are crucial elections and a lot is at stake for Iraq."
Al-Hashemi's veto led to portracted negotiations and threatened to further delay elections.
According to al-Attiya, the law will expand parliament from 275 seats to 325 seats, 310 of which will be allotted to Iraq's 18 provinces, with the remainder reserved for religious minorities and blocs that garnered national support but did not win seats.
The differences over representation had led to fears of further sectarian division in Iraq ahead of the polls.
'No population data'
Ala al-Talabani, a Kurdish member of parliament, told Al Jazeera that poor population statistics in Iraq complicated the allotment of seats in parliament.
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 new law was reportedly brokered by UN and US embassy officials [GALLO/GETTY]
"The problem is that in Iraq, we don't have fixed data of the population in 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.
No definitive election date has yet been set. The polls, originally scheduled for January 16, have been delayed because of the failure by MPs to initially agree on the new law.
The United Nations has proposed February 27 as the most "feasible" date for parliamentary elections, nearly a month later than the deadline set by the constitution.
In principle, the constitution requires that the poll, the second since a US-led invasion ousted Saddam in 2003, be held by the end of January.