Top U.S. and Iraqi diplomats warned Thursday of a rising threat in Iraq from al-Qaida, which is carrying out suicide and car bombings with greater frequency nearly two years after U.S. troops withdrew from the country.

A wave of car bombs hit the Iraqi capital Thursday, killing 33 people and wounding dozens just as Secretary of State John Kerry and Iraqi Foreign Minister Hoshyar Zebari were meeting to discuss how to stop Iraqi airspace from being used to ferry weapons and illicit cargo from Iran to the Syrian government.

Because of Iraq’s recent spike in violence, both Kerry and Zebari agreed that stemming the flow of weapons and militant fighters from neighboring Syria was a significant step that had yet to be made.

More than 3,000 people in Iraq have been killed during the past few months, including 69 who died last weekend in a series of car bombings targeting those celebrating the end of Ramadan.

“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.

In 2011 and 2012 there was an average of five to 10 suicide bombings a month, according to a senior administration official familiar with Kerry’s talks with his Iraqi counterpart. They have averaged about 30 in each of the past three months and it’s suspected that the suicide attackers are mostly coming from Syria, indicating a fairly sophisticated al-Qaida network, the official said on condition of anonymity.

The official said the U.S. wants to share intelligence and help the Iraqis map the network and disrupt its financing. Also, the U.S. is encouraging Iraq to make precision attacks against perpetrators to avoid aggravating the fragile security situation in the country by rounding up too many people or targeting the wrong person.

The overflights in Iraq, which is sandwiched between Iran and Syria, long have been a source of contention between the U.S. and Iraq.

Iraq and Iran claim the flights are carrying humanitarian goods, but American officials say they are confident that the planes are being used to arm and support Syrian President Bashar Assad’s fight against U.S.-backed opposition forces.

In 2012, then-Secretary of State Hillary Rodham Clinton secured a pledge from Iraq to inspect the flights, but until March when her successor, Kerry, visited Baghdad, only two aircraft had been checked by Iraqi authorities, according to U.S. officials.

Congress recently was notified that a $2.6 billion air defense system was being sold to the Iraqis to help them better control their airspace, but it won’t be operational for some time, the administration official said. The Iraqis also are getting a shipment of F-16 aircraft from the U.S. in the fall.

The official said that since March there has been a disruption in the overall frequency and number of what the U.S. suspects is illicit cargo transfers, but that much work is needed to curb the problem. The official said, however, that no illicit cargo or weapons had been intercepted.