Jeb Bush just made a big break from many of his GOP rivals

Former Florida Gov. Jeb Bush (R) separated himself on Tuesday from some of the absolutist anti-Syrian refugee positions being offered by his Republican presidential rivals.

During an interview with Bloomberg Politics, Bush said "if there's any kind of concern," refugees should not be allowed in.

"But I don't think we should eliminate our support for refugees. It's been a noble tradition in our country," he added.

Bush also expressed empathy for people who are "legitimately concerned about ... the competency of the Obama administration as it relates to screening processes."

After last week's terror attack in Paris, a wide swath of Republicans stated their vociferous opposition to the US accepting any refugees fleeing the violence in Syria. A slew of governors said they would try to stop any refugees from entering their states, but it is not clear they have the legal authority to do so.

The Paris attack was linked to the Islamic State group (also known as ISIS), which has been one of the major combatants in the Syrian civil war that is leading to the refugee crisis there.

Critics of President Barack Obama's plan to accept thousands of the refugees have been raising the possibility of the Islamic State infiltrating the refugee population and carrying out another attack in the US. New Jersey Gov. Chris Christie (R), another presidential candidate, said Monday that he wouldn't even support letting in orphan refugees under the age of 5.

"The answer to this is not to ban people from coming," Bush told Bloomberg's Mark Halperin and John Heilemann for their "With All Due Respect" show.

"The answer is to lead, to resolve the problem in Syria. That's the ultimate answer," he added. "And that's my focus."

On Monday, Obama appeared to criticize Bush and another presidential candidate, Sen. Ted Cruz (R-Texas), for their "shameful" comments supporting special protections for Christian refugees in Syria. But Bush said he wasn't dissuaded from his position.

"He didn't mention my name, but yeah," Bush said when asked if he interpreted Obama's comments as a direct shot at him. "I've had this view for a long while that religious minorities in the Middle East and around the world are deserving of our support."

Bush also said he disagrees with Cruz, who wants to specifically bar Muslim refugees from Syria.

Check out the full Bloomberg Politics report on Bush's interview >