State TV said parliament will convene on June 12 to discuss the request.
Fighters believed to be affiliated with the Islamic State in Iraq and the Levant (ISIL) seized key buildings in the northern city of Mosul late on June 9.
Officials said dozens of heavily armed insurgents seized the provincial capital's headquarters, occupied police stations, overran the airport, and freed prisoners from jails.
The governor of the northern province of Nineveh, Athil al-Nujaifi, said the military and police forces abandoned their positions.
Residents were quoted as saying that black flags associated with jihadist groups were flying from buildings and that the militants had announced over loudspeakers that they had come to "liberate" the city of nearly 2 million people.
Earlier on June 9, Governor Nujaifi made a televised plea to the city's inhabitants to fight the Al-Qaeda-linked militants who have been regaining ground in Iraq.
Nujaifi escaped Mosul unharmed before the provincial government's headquarters fell.
His brother, parliament speaker Osama al-Nujaifi, called on the Iraqi government and the regional government of Kurdistan to send reinforcements to Mosul. He also said he had asked the U.S. ambassador for help.
"When battles intensified inside the city of Mosul, the [Iraqi] forces abandoned their weapons and the commanders fled, leaving behind weapons and armored vehicles -- their positions were easy prey for terrorists, even the Mosul airport," parliament speaker Nujaifi said in Baghdad.
"Planes and command positions -- all of them have fallen in addition to weapons caches. Also prisons were stormed and criminals have been set free. What happened is a catastrophe by any measure."
Tens Of Thousands Flee Fighting
The president of the semiautonomous northern Kurdistan region, Masud Barzani, called on international organizations to provide humanitarian assistance.
United Nations Secretary-General Ban Ki-moon's spokesman Stephane Dujarric said the UN chief is "gravely concerned" by the serious deterioration of the security situation in Mosul.
U.S. State Department spokeswoman Jen Psaki also voiced concern over what she called the "extremely serious situation" in Mosul.
RFE/RL correspondents in Iraq report that the fighting has forced thousands of people to flee their homes to other parts of the province and beyond.
Citing data from the International Organization for Migration, a UN spokesman said an estimated 500,000 people have fled Mosul.
WATCH: Thousands of people have fled Mosul after Islamist militants seized control of one of the city. Displaced families wait in long lines before their cars were allowed to cross into neighboring Dohuk Province, north of Mosul.
"We woke up today in the morning and the streets were empty from security forces, from check points and the army. They were all gone. Nothing is happening now. All the streets are opened now. Some clashes took place in the morning but now there is nothing," one Mosul resident told RFE/RL.
"[The armed men] entered [Mosul] but they didn't do anything. They asked people not to be afraid because they are not coming to hurt them," he continued.
"But our people are always afraid. Many of them left their homes and then returned to them because they were not accepted by [Iraq's autonomous Kurdistan region]. Now it's calm, there are cars in the streets. The army and the police have left and [the armed men] are now controlling the city."
Meanwhile, the Turkish Consulate in Mosul confirmed reports that 28 Turkish truck drivers carrying diesel to Mosul had been abducted.
A former Al-Qaeda stronghold, Mosul is located 360 kilometers northwest of Baghdad.
Fighters of the Islamic State in Iraq and the Levant (ISIL) and their allies have recently carried out attacks across western and northern Iraq.
Security forces are trying to dislodge ISIL fighters from the western province of Anbar, where they have been holding parts of the provincial capital, Ramadi, and much of the nearby city of Fallujah since January.
ISIL militants attacked the university campus in Ramadi, the capital of Anbar Province on June 7 and are still holding at least 15 Anbar University staff members hostage
Fierce clashes were also reported on June 9 in the city of Fallujah and the nearby town of Garma, also in Anbar Province.
WATCH: Iraqi security forces battled with Al-Qaeda-linked insurgents in Anbar Province on June 7-8.
The UN's refugee agency, the UNHCR, said on June 7 that the number of people driven from their homes by months of fighting in Anbar had now reached close to 480,000.
Due to the ongoing violence, there was no voting in Anbar in Iraq's parliamentary elections on April 30.
Iraq is witnessing bloody violence at the highest level since 2006-07, when tens of thousands were killed in a sectarian conflict between the Shi'ite majority and Sunni minority.
According to the United Nations figures, some 900 people were killed in violence across Iraq in May.