"I think that in this phase, it is critical that we build bridges to American Muslim communities, not vilify them, not drive them into the shadows, and encourage them to work with us," Johnson said during an interview on MSNBC's "Morning Joe," where he was pressed on Trump and Cruz.
"I believe that inflammatory comments about patrolling and securing Muslim neighborhoods or barring Muslims from entering this country, having an immigration policy based on religion, is counterproductive to our homeland security and national security interests," he added.
Cruz caught flak last week after suggesting that the U.S. "patrol" Muslim neighborhoods following the terrorist attacks in Brussels, which were claimed by the Islamic State in Iraq and Syria (ISIS). He has since feuded with New York Police Commissioner Bill Bratton over the call to monitor Muslims.
Trump claimed that Brussels was the latest example of the U.S. needing to more vigorously vet those refugees entering the country when fleeing violence in Syria. He has seen months of criticism over his proposal to temporarily ban Muslims from traveling to the U.S., though a poll this week found half of voters support it, including seven in 10 Republicans.
Johnson said Tuesday that U.S. officials remain vigilant and continue to be "very concerned" about efforts to carry out a terrorist-inspired plot in the United States, saying they represent a "new era" of attacks.