A pair of former presidential national security advisers on Wednesday pushed lawmakers to increase airstrikes in Iraq and Syria with possible boosts in U.S. ground forces in the fight against the Islamic State group.

But they also argued that moves to limit or halt the flow of refugees from those countries to America send the wrong message to would-be allies in the region, feeding into Islamic State propaganda of a religious war against the West.

"If there are fixes at all in this, they will not be quick," warned Ryan Crocker, former U.S. ambassador to both Iraq and Afghanistan. "Military actions can establish a contest that is more favorable to a political solution than is there right now."

In testimony before the House Armed Services Committee, Crocker argued for a no-fly zone over much of the region and a safe zone for refugees in Syria to provide immediate relief to those fleeing the terrorist group. He also said military officials should "amp up the air campaign" against the enemy's fighters and infrastructure.

However, he also repeated the White House mantra that a long-term solution in the region depends more on political success than military might.

Former CIA director John McLaughlin echoed that idea, but added that ignoring or lessening the role of the U.S. military in the region is also a dead-end solution.

"We cannot settle the problems in Iraq militarily, but we cannot solve them without a military component, either," he said.

Testimony from the two longtime security officials was scheduled before the terrorist attacks in Paris last Friday, but plays into broader work by the committee and House leadership task force working to "keep America safe and to bolster efforts to eliminate ISIS."

Defense Secretary Ash Carter and top military officials are scheduled to testify before the committee Dec. 1 on progress and setbacks in the fight.

Meanwhile, congressional Republicans are pushing for a halt in the refugee admission program out of fear that it could lead to a terrorist attack on American soil.

Crocker and McLaughlin pushed against that, arguing that refusing Muslim refugees would create more political problems than security benefits for the U.S.

"We have to show we are not fighting against Sunnis," said Crocker, arguing for an increase in the number of refugees admitted, rather than a decrease. "It's a way we can blunt the accusations that we are the enemy of Arabs and Muslims."

President Obama has come under increasing criticism for the refugee vetting program, and for his overall strategy in the region.

McLaughlin called ISIS a bigger, more organized threat than al-Qaida and said it should be the administration's top security focus.

"Instead of trying to get rid of (Syrian president) Bashar al-Assad and ISIS at the same time, we need to say ISIS comes first," he said, using an alternative name for the Islamic State group.

Crocker called the conflicts in the region "unprecedented chaos" even for the Middle East.

Syria, Yemen and Libya are essentially failed states now, and Iraq is dangerously close to that point, he warned.

"You can hope that the Islamic State twisted ideology is the next to fail in the region, but hope is a poor policy," he said.