Donald J. Trump issued another call for more scrutiny of mosques in the United States as fresh fears of terrorism, spurred by the attacks in Paris, dominated the presidential campaign conversation on Monday.

Mr. Trump, who said last month that he would be open to shutting down mosques as part of the fight against Islamic State militants, reiterated on Monday that the idea should be “studied.” Mr. Trump’s concerns about radical Islam were echoed by another leading Republican presidential candidate on Monday. Ben Carson, who has been running close with Mr. Trump atop many polls, called on Congress to defund its program to give safe passage to Syrian refugees. The retired neurosurgeon also suggested that Muslim clerics should be pressured to condemn the Islamic State, also known as ISIS or ISIL.

The suggestion of basing refugee status on religion offended President Obama on Monday. Speaking at a news conference in Turkey, he called the idea un-American.

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