Khudeir al-Khuzaie statement ordered the new parliament to hold its first session on Tuesday and to be chaired by the eldest member.
Constitutionally the next step would be to elect a speaker and two deputies, then within 30 days to choose a new president who in return has 15 days to ask the largest bloc to choose a prime minister and form the new government. The Prime Minister-designate has 30 days to present his cabinet to the parliament within 30 days. Absolute majority is needed to approve new government inside parliament.
Led by al-Qaida spin-off group known as the Islamic State of Iraq and the Levant, the insurgents quickly took over Iraq's second-largest city of Mosul on June 10 followed by Saddam Hussein's hometown of Tikrit and smaller communities in the northern Sunni heartland as government forces melted away. The latest onslaught poses a daunting challenge and threatens to split the nation up into warring Sunni, Shiite and Kurdish enclaves.
Al-Maliki has faced pressure, including from his onetime Shiite allies, to step down and form an interim government that could provide leadership until a more permanent solution can be found. He has insisted the political process must be allowed to proceed following April elections in which his bloc won the largest share of parliament seats
British Foreign Secretary William Hague's trip follows a visit by U.S. Secretary of State John Kerry, who earlier this week delivered a similar message and warned that Washington is prepared to take military action even if Baghdad delays political reforms.
The intense diplomatic push underscores the growing international concern over the gains by fighters led by the Islamic State of Iraq and the Levant, the Sunni extremist group that has seized large swaths of Iraq and seeks to carve out a purist Islamic enclave across both sides of the Syria-Iraq border.
Hague called the group a "mortal threat" to Iraq that also posed a threat to others in the region, according to a statement from his office. He was due to meet al-Maliki, Kurdish regional President Massoud Barzani and other political figures later Thursday.
"The immediate priority, and the focus of my discussions today, is to help and encourage Iraqi leaders to put sectarian conflict behind them and unite across all political parties," he said.
Britain has ruled out military intervention in Iraq, but Hague said it would provide "diplomatic, counter-terrorism and humanitarian support." The U.S. is sending 300 military advisers, although Kerry stressed that Baghdad needs to take steps to ensure that Iraq's military can defend the country without relying on outside forces.
Also Thursday, hundreds of Iraqi villagers continued to flee advances by Sunni militants to the northern self-ruling Kurdish region and crowded at a checkpoint, seeking shelter in the relative safety of the self-rule region.
An insurgent artillery offensive against Christian villages in the north of Iraq on Wednesday sent thousands of Christians fleeing from their homes, seeking sanctuary in the Kurdish enclave. The shelling of the a cluster of villages happened in an area known as Hamdaniya, 45 miles (75 kilometers) from the frontier of the self-ruled Kurdish region.
While many villagers appeared to have been granted access by daybreak, hundreds of Shiite refugees were still hoping to be let in but were facing delays because they lacked sponsors on the other side.
One of the refugees, who gave only her nickname of Umm Alaa, fearing retribution, said she and hundreds of others with her had left their village of Quba and another nearby hamlet during the militants' initial assault on June 10 to seek shelter in nearby communities that were then attacked Wednesday. Another, who agreed to be identified only named Huda, tried to calm her 10-year-old son Mohammed, who was crying of thirst.
"They will kill every Shiite man, and they will burn every Shiite house. Nobody has stayed in Quba. Every single Shiite has left," he said, echoing the fears of many interviewed Thursday.
A spokesman for the United Nations refugee agency, Adrian Edwards, last week said the number of people in Iraq forced from their homes is estimated to be 1 million so far this year.
Hadid reported from Irbil, Iraq. Associated Press reporters Hamza Hendawi, Qassim Abdul-Zahra and Sameer N. Yacoub in Baghdad contributed to this report.