Trump has called for a mandatory database to track Muslims in the US and Carson has compared Syrian refugees to rabid dogs.
The comments follow last week's Paris terror attacks that killed more than 130 people and wounded hundreds more. Isis has claimed responsibility, elevating fears of attacks in the US and prompting calls for new restrictions on refugees fleeing Syria.
Trump's comments are expected to force his rivals to give their views. Republicans have vacillated in handling of inflammatory comments from the bellicose billionaire.
Former Florida Governor Jeb Bush was the first Republican rival to condemn Trump's call for a Muslim database, calling the proposal "abhorrent".
Trump's comments about a national database for Muslims came while he was campaigning in Iowa. Trump and retired neurosurgeon Carson have stunned the political world with their rise to the top of some polls in the crowded Republican nomination race. With the first primary votes less than three months away, the two outsiders continue to overshadow established politicians such as Bush, the son and brother of former presidents who was expected to be an early favourite.
Many Democratic insiders have said they would prefer the Republicans nominate Trump or Carson, considering them easier to beat in the general election, still a year away. Democrats have increasingly consolidated behind Hillary Clinton, who faces two opponents for her party's nomination.
Carson also raised eyebrows when he compared blocking terrorists posing as refugees from entering the US to handling a rabid dog.
"If there's a rabid dog running around in your neighbourhood, you're probably not going to assume something good about that dog," Carson told reporters in Alabama.
The Council on American-Islamic Relations condemned both Trump and Carson's comments as "Islamophobic and unconstitutional."
