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Secretary of State John Kerry told his Iraqi counterpart Thursday that Iraq must stop weapons from flowing through its airspace to arm the forces of embattled Syrian President Bashar Assad.

Iraq and Iran claim the flights are carrying humanitarian goods, but the U.S. is confident that air shipments — along with material being trucked across Iraqi territory from Iran to Syria — are helping Assad's regime cling to power by increasing its ability to strike Syrian rebels and opposition figures demanding his ouster. The issue has long been a source of contention between the U.S. and Iraq, and Kerry raised it again during a meeting at the State Department with Iraqi Foreign Minister Hoshyar Zebari.

Kerry also said the two discussed weapons that are flowing out of Syria for use against Iraqis.

"It's a two-way street. It's a dangerous street," Kerry said.

He said some progress has been made to curtail the movement of weapons but that he and Zebari agreed that "there is very significant progress yet to be made."

Zebari emphasized that Iraq was taking a neutral position on the Syrian crisis. He said Iraq had not provided arms, money or oil to the Syrian regime and said Iraqis were not going into Syria to fight with the consent of the Iraqi government.

"Iraq is a reliable, a dependable ally and partner for the United States," Zebari said.

Both noted rising sectarian violence in Iraq, nearly two years after U.S. troops withdrew from the country.

Attacks have been on the rise since a deadly security crackdown in April on a Sunni protest camp. More than 3,000 people have been killed in violence during the past few months, raising fears Iraq could see a new round of widespread sectarian bloodshed similar to that which brought the country to the edge of civil war in 2006 and 2007.

On Thursday, a wave of car bombs hit the Iraqi capital, killing 33 people and wounding dozens. There was no claim of responsibility, but Sunni extremists such as al-Qaida's arm that seek to undermine the Shiite-led government are frequently blamed for attacks targeting civilians.

"Iraq sits at the intersection of regional currents of increasingly turbulent, violent and unpredictable actions," Kerry said. "Sunni and Shia extremists on both sides of the sectarian divide throughout the region have an ability to be able to threaten Iraq's stability if they're not checked.

"And al-Qaida, as we have seen, has launched a horrific series of assaults on innocent Iraqis, even taking credit for the deplorable bombings this past weekend that targeted families that were celebrating the Eid holiday. And this al-Qaida network, we know, stretches well beyond Iraq's borders."

Kerry said many al-Qaida leaders were currently operating in Syria and said the U.S. and Iraq must work faster to find a diplomatic resolution to the conflict in Syria.

Zebari acknowledged the upswing in violence in Iraq, but he said the nation was not undergoing a civil or sectarian war.

"In recent months, as you have seen, and in recent days, in fact, we have seen the renewal of violence, of terrorist attacks by al-Qaida more frequently," Zebari said. "It has cost many, many lives. But despite all these attacks, the Iraqi people have not succumbed, in fact, to these atrocities."

Kerry said he and Zebari talked about Iran and Hezbollah's efforts to fuel conflict in the region.

"We agreed that we cannot allow them to play on the sectarian divides to recruit young Iraqis to go fight in a foreign war the same way that we cannot allow al-Qaida and other extremists to recruit young men from Iraq and elsewhere to join into their twisted version of jihad," Kerry said. "So we are committed to helping Iraq to withstand these pressures and to bolster the moderate forces throughout the region."