WATCH: Obama's Awkward Moment With Iraq's PM

In footage caught by CBS, President Obama appears to ignore Iraqi PM Haider al-Abadi, on the same day he acknowledges that the Pentagon has yet to finalize a plan with the Iraqi government to combat ISIS.

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ELMAU, Germany AP - Acknowledging military setbacks, President Barack Obama said Monday the United States still lacks a "complete strategy" for training Iraqi forces to fight the Islamic State. He urged Iraq's government to allow more of the nation's Sunnis to join the campaign against the violent militants.

Nearly one year after American troops started returning to Iraq to assist local forces, Obama said the Islamic State remains "nimble, aggressive and opportunistic." He touted "significant progress" in areas where the U.S. has trained Iraqis to fight but said forces without U.S. assistance are often ill-equipped and suffer from poor morale.

IS fighters captured the key Anbar provincial capital of Ramadi last month, prompting Defense Secretary Ash Carter to lament that Iraqi troops lacked "the will to fight." That was a strikingly negative assessment of a military that has been the beneficiary of billions in U.S. assistance dating back to the war started during the administration of U.S. President George. W. Bush in 2003.

Still, Obama indicated that simply increasing the number of Americans in Iraq would not resolve the country's issues. The U.S. currently has about 3,000 troops there for train-and-assist missions.

"We've got more training capacity than we have recruits," he said at the close of a two-day Group of Seven meeting at a luxury resort tucked in the Bavarian Alps.

G-7 leaders invited Iraqi Prime Minister Haider al-Abadi to join them Monday for talks on the security situation in the Middle East. Obama and Abadi also met one-on-one shortly before the president departed for Washington.

In both public and private, Obama urged Abadi and his Shiite-led government to allow more Sunnis to fight the Islamic State. The White House has long blamed Iraq's sectarian divisions for stoking the kind of instability that allowed the militants to thrive.

"We've seen Sunni tribes who are not only willing and prepared to fight ISIL, but have been successful at rebuffing ISIL," Obama said by the U.S. government. "But it has not been happening as fast as it needs to."

In Washington, the highest-ranking Sunni in Iraq's government said Sunni tribes are still receiving insufficient training and inferior weapons compared to the national army. Parliament Speaker Salim al-Jabouri put the onus for fixing that on Baghdad, saying it should provide clear assurances that the tribes will receive the necessary weapons.

"Guarantees create confidence, and we need confidence," al-Jabouri told a small group of reporters, speaking through an interpreter.