Iraq is open to greater American military cooperation as U.S. commanders explore ways to boost security assistance to the country, a top Iraqi official said Thursday as a fresh wave of bombings claimed 16 lives.

The Chairman of the U.S. Joint Chiefs of Staff, Gen. Martin Dempsey, has recommended that military American commanders look for ways to help improve the military capabilities of Iraq and Lebanon, which both face the risk of spillover from the civil war in neighboring Syria.

Dempsey said Wednesday that the assistance would not involve sending U.S. combat troops, but could involve the U.S. sending training teams and accelerating sales of weapons and equipment.

The last American combat troops left Iraq in December 2011, ending a nearly nine-year war that cost nearly 4,500 American live and left more than 100,000 Iraqis dead.

About 100 military and civilian Department of Defense personnel remain in Iraq as an arm of the American Embassy to act as liaisons with the Iraqi government and facilitate arms sales. The U.S. has similar offices in other countries.

Ali al-Moussawi, the media adviser for Iraqi prime minister Nouri al-Maliki, said Baghdad would welcome increased arms sales and faster weapons deliveries along with U.S. training teams to help it confront rising regional instability and terrorist threats.

“We welcome this kind of cooperation and we consider it a part of the existing agreement between us,” al-Moussawi said when asked about Dempsey’s comments. “Because of the high risks the region faces, I think there should be bigger cooperation and coordination between all countries threatened by terrorism.”

Iraq is struggling to contain a resurgent al-Qaida that is one of the main drivers behind the country’s worst uptick in violence in half a decade. More than 2,000 people have been killed in car bombings and other violent attacks in Iraq since the start of April.

More violence rocked Iraq late Thursday when bombs struck cafes in and around Baghdad, killing 16 and wounding dozens. The attacks struck in quick succession at the start of the local weekend while the cafes were filled with patrons watching a soccer match.

Police reported five people dead and 17 wounded in Baghdad’s largely Sunni neighborhood of Azamiyah, and another three dead and 14 wounded in Shiite-dominated Umm al-Maalif, in the southwestern suburbs of the capital.

Another blast struck the Shiite town of Jbala, about 35 miles south of Baghdad, killing 8 and wounding 25.

The upsurge in violence comes as Iraqi fighters have been traveling to fight on both sides of Syria’s civil war. The Iraqi branch of al-Qaida is pushing to make itself a player in the conflict, and now calls itself the Islamic State of Iraq and the Levant to highlight its cross-border ambitions.

Iraq has acquired billions of dollars’ worth of American-made military equipment, including howitzers, armored personnel carriers and Abrams tanks in recent years.

It has yet to receive the first of as many as 36 F-16 fighter jets it has ordered, and Baghdad has been pressing U.S. officials to speed delivery of the warplanes.