Graham, R-S.C., said on State of the Union Sunday that Maliki should resign to help quell the sectarian conflict between his Shiite ruling party and the al-Qaida-affiliated Islamic State of Iraq and Syria militants, supported by the Sunnis.
"Stop the march on Baghdad. Form a new government. There are plenty of voices over there," Graham said. "He should resign. He is incapable of bring the Sunnis back into the fold."
Graham said there were warnings ISIS's invasion over the border of Syria was coming.
"Al-Qaida in Iraq... was on their back, just about gone" when Obama took office, Graham said. "They got what they wanted. The Obama administration wanted to say 'I ended the war in Iraq and I'm going to end of the war in Afghanistan.' This is predictable as the sun rising in the east."
The Obama administration is weighing how to respond to ISIS's takeover of the cities of Mosul and Tikrit, including airstrikes. ISIS appears poised to attack Iraq's capital Baghdad, and Monday, the militant group claimed it had executed some 1,700 Iraqi soldiers.
The president said there would be "no boots on the ground," and Secretary of State John Kerry said he wouldn't rule out cooperation with Iran, although the Pentagon denied it was planning to coordinate with Tehran.
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