Meeting Iraqi Foreign Minister Hoshyar Zebari, Kerry said that Iraq faced "increasingly turbulent, violent and unpredictable" regional currents.
"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," Kerry told reporters.
Kerry condemned the "horrific series of assaults" by Al-Qaeda, including Sunday's attacks that killed 74 people during the Eid al-Fitr holiday.
An Al-Qaeda front group took credit, saying that Shiites "will not dream of security during night or day, during Eid or other" days.
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"With many Al-Qaeda leaders now operating in Syria, we all need to accelerate our work in order to set the conditions for diplomatic settlement for the Syrian crisis," Kerry said.
The United States, along with Sunni monarchies Qatar and Saudi Arabia, has supported the rebels but says it only provides non-lethal assistance.
The United States has pledged further aid to the rebels after concluding that Assad used chemical weapons.
Assad receives support from Iran, a Shiite theocracy and US adversary, and the Lebanese Shiite movement Hezbollah.
Kerry said he would talk to Zebari about weapons both going in and out of Syria.
"It's a two-way street. It's a dangerous street," Kerry said.
Zebari said that Iraq was pursuing "an independent and neutral position" on Syria.
"We kept our distance on both sides of the conflict and Iraq has not provided arms, money or oil to the Syrian regime," he said.
Zebari said that Iraq is "not having a civil or sectarian war," calling Al-Qaeda a global threat.