Rep. Duncan Hunter wants the Pentagon to directly provide weapons to vetted fighters.
The United States and Iraq are engaged in a heated blame game over the fall of Ramadi.
The decision comes amid ISIS gains in Iraq.
"We still believe the strategy is working," Pentagon spokesman Army Col. Steve Warren said.
Ramadi was a hotly contested battleground for U.S. troops during the war.
Defense Secretary Ashton Carter said he opposes a push to bypass the Iraqi government.
A top U.S. general said the strikes against the terror group in Iraq were making an impact.
"Bombing missions must be quicker," Prime Minister al-Abadi says.
The strike was conducted by two Canadian CF-18 Hornets against an ISIS garrison.
Canada's vote comes as Congress is stalled on efforts to authorize force.
It is the first time a U.S. soldier has been hurt by direct fire in the anti-ISIS campaign.
Kerry denied that the anti-ISIS strategy is taking a back seat to the nuclear talks.
The administration is sticking by its plan to train Iraqi forces, despite Ramadi's fall.
The Pentagon doubled down on Secretary Carter's criticism of Iraqi forces.
All Iraqi forces left Ramadi early Tuesday morning.
The top Democrat on the House Intelligence Committee called Ramadi's fall to the Islamic State in...
Neither would former President George W. Bush, Rubio insisted on Wednesday.
The comments came after meeting with Baghdad officials over the weekend.
The bombing killed three people Friday. No U.S. personnel were hurt in the blast.
The Islamic group has gained ground in Syria, however.
Iraqi Prime Minister Haider al-Abadi said the city of Tikrit has been liberated.
The move could bring the U.S. closer to cooperation with Iran.
The U.S. military is training and equipping 5,000 Syrian rebels to fight the Islamic State in Iraq...
The announcement on Tuesday marks the second time the coalition has officially declared territory...