Correction: An earlier version of this story incorrectly said that Sunni-backed parties won a majority of parliamentary seats in Iraq’s last election. They won a plurality in the 2010 vote, not a majority. This version has been corrected.

Iraqi Sunnis hope to leverage their cooperation in the fight against a new al-Qaeda insurgency in western Iraq to win political space that they say has been denied to them by the Shiite-led government of Prime Minister Nouri al-Maliki, the country’s senior Sunni politician said Thursday.

“The idea is we need to give greater authorities to the Sunni provinces” and make Sunni tribal fighters “an integral part of [Iraq’s] military force,” said Osama al-Nujaifi, the speaker of parliament.

Nujaifi, on a week-long visit to Washington, met Wednesday with President Obama and Vice President Biden. He said he and the Obama administration are “in total agreement” about the need to arm Sunni tribal recruits and permanently integrate them into the Iraqi armed forces.

The administration has agreed to expedite arms sales to Iraq in the hope that its security forces will regain control of Anbar province’s two main cities, Fallujah and Ramadi, from militants with al-Qaeda’s Iraq affiliate, which also operates in Syria.

The administration notified Congress on Thursday of plans to sell an additional 500 Hellfire missiles to Iraq, at a cost of $82 million. The United States, Iraq and Jordan have said that they are considering training for Iraqi forces by about 1,500 American troops based in Jordan.

With Maliki’s agreement, the administration is also seeking to re-create the Sunni “Awakening” of 2006-2007, when Sunni tribesmen in Anbar received arms and money directly from the U.S. military to subdue militants in the province. The new arms are to be funneled through the Iraqi government.

Nujaifi and other Sunni leaders support the plan but reject a repeat of what they say happened shortly after U.S. forces left Iraq in late 2011. They allege that the Maliki government abandoned, disarmed, persecuted and, in some cases, jailed the tribal fighters, ignoring promises to integrate them into the country’s security forces.

Now, Nujaifi said in an interview, “these tribes have to become the force that defends Anbar, not just as part of this phase, not on a part-time basis.”

The amount of face time that Nujaifi got with top U.S. officials — including Secretary of State John F. Kerry and Defense Secretary Chuck Hagel — suggested that Washington realizes that mobilizing Iraq’s beleaguered Sunni community will be key to restoring order in Anbar. A State Department official said Washington is hopeful that the ongoing crisis might deliver a larger breakthrough in Iraq’s stagnant politics.

“A big part of what Nujaifi and we are trying to do is move this beyond the military front,” said the official, who was not authorized to speak publicly about the situation. “Even if you can quell the al-Qaeda advances long-term, you won’t be able to make any progress without political reform as well.”

Nujaifi, who became speaker in 2010, said he conveyed to U.S. officials that Maliki is primarily to blame for the rising violence and militancy in the country. Many Sunnis regard the prime minister as autocratic and concerned mainly with appeasing political allies, most of whom are religious Shiites.

“I feel the greatest responsibility lies with the Iraqi government in terms of how the country has turned out,” said Nujaifi, who described entrenched sectarianism and “a sense of despondency [and] feeling of hopelessness in society.”

Public protest against the government grew in Anbar throughout last year. But it wasn’t until December, when Maliki ordered a crackdown on demonstrators in Ramadi, that al-Qaeda made its move, Nujaifi said. “The entire region rejects al-Qaeda,” he said. But the residents dislike the Shiite-dominated Iraqi military even more, he said, and “regard al-Qaeda as the lesser of two evils. They hate it, but they’re not willing to fight it.”

Nujaifi said that he had not spoken to Maliki in more than a month and that the prime minister “almost never discusses any security issues with parliament.”

“In the recent crisis, he consulted no one,” Nujaifi said.

While Iraqi forces have stayed outside Fallujah, government aircraft have bombarded the restive areas. The government has said that dozens of militants have been killed. But Nujaifi said the airstrikes had brought about only “the displacement of many thousands of people.”

He said the al-Qaeda fighters in Fallujah, which he estimated at no more than 200, have settled into an uneasy coexistence with tribal chiefs in the city. Last week, Nujaifi said, al-Qaeda militants detained but soon released a newly appointed interim police chief and members of a city council backed by tribal leaders.

“I have total confidence that al-Qaeda will be driven out,” he said, “but we can only achieve that if proper assurances are offered” to local tribesmen. Among the ways that Maliki could build confidence among them, he said, was to release Sunni detainees not linked to al-Qaeda who have been imprisoned for bearing arms in the past.

The crisis in Anbar is all but certain to become a dominant theme in Iraq’s parliamentary election in April, the country’s first since the U.S. pullout.

Maliki, who has made restoring security the bedrock of his political brand, is likely to face mounting scrutiny the longer al-Qaeda cells operate openly in Iraqi cities. In recent months, under heavy U.S. pressure, he has made certain concessions and overtures to Sunni leaders in hopes of restoring order in the western part of the country.

Sunnis could gain from the crisis if they manage to form alliances with moderate Shiites and Kurds before the polls. Nujaifi is seeking to rebuild a coalition of Sunni-backed parties similar to the one that won a plurality in the 2010 election.