"Because the forces we've trained are performing better than expected, we feel it's in everyone's interest to train more."
Warren acknowledged that an expanded training effort -- if approved -- could require additional American troops deploying to Iraq, beyond the current force of roughly 3,000 advisers and trainers.
Defense officials told AFP several hundred additional US forces might be required.
"It's very incremental," a defense official said on condition of anonymity.
A ramped up training program could mean deploying "less than a thousand" troops at most, as well as increasing the number of training sites from the four currently being used, the official said.
The training effort would carry "a particular emphasis on the Sunnis," the official said.
Iraq's Sunni community has yet to join the fight against the IS group in large numbers, amid lingering distrust of the Shiite-led government in Baghdad. And the IS jihadists have sought to exploit the Sunnis' sense of alienation from Baghdad.
Until now, the Baghdad government has overseen the training of Sunni tribal fighters and Washington has been frustrated at what it considers the slow pace of the program.
But for the first time, the Obama administration is now looking at American troops directly training Sunni volunteers.
Weapons deliveries to the Sunnis, however, would continue to flow through the Iraqi central government.
- No talk of spotters -
The administration was looking at a mere "refinement" of the current strategy, which has relied on US-led air power in support of local forces on the ground, officials said.
And there was no serious talk of sending forward air controllers to the front with Iraqi or Kurdish forces, or of dramatically expanding the American military presence.
Republican lawmakers have blasted Obama over his approach to the conflict, with some hawks demanding a more aggressive stance that would include spotters on the ground to direct bombing raids and a larger-scale air war.
Although the US military was considering broadening its training effort, Iraqi Prime Minister Haider al-Abadi's government has had difficulties providing enough recruits for courses and ensuring units show up properly equipped, officials said.
"We'd like to see... more Sunnis come into the pipeline and be trained," Warren said. "This is what we have urged Abadi to help solve."
After meeting Abadi on Monday in Germany, Obama said the Iraqi side needed to show it could make use of extra help being offered by the United States and other members of the anti-IS coalition.
"All the countries in the international coalition are prepared to do more to train Iraq security forces if they feel that additional work is being taken advantage of," Obama said on the sidelines of the G7 summit.
"And one of the things we're still seeing in Iraq is places where we have more training capacity than we have recruits."
Obama said he was waiting for final plans to be presented by the Pentagon.
US concerns about the Iraqi army's ability to absorb the training were highlighted by the absence of trainees at al-Asad air base in Anbar province, where several hundred American troops are stationed to help with combat instruction.
The Pentagon said Baghdad had pulled out the trainees and redeployed them to help provide security for a religious pilgrimage.
The US-led coalition has trained 8,920 Iraqi troops so far in basic combat skills and 2,601 are going through courses now.
The US-trained troops have deployed to Samarra, north of Baghdad, to a front line in the north with Kurdish peshmerga forces, and in al-Karmah in Anbar province, Warren said.
Other units that completed the training are at the ready for an eventual counterattack to retake the western city of Ramadi, which fell to IS jihadists on May 17.