 -- Denying Muslims entry into the United States would be “counterproductive” and “would not work,” the U.S. Secretary of Homeland Security said today of calls to take such action.

It is more important to “build bridges” with American-Muslim communities in the wake of the most recent mass shooting in Florida, Secretary Jeh Johnson told ABC News’ George Stephanopoulos.

“Overly simplistic suggestions that we ban people from entering this country, based on religion, or ban people from an entire region of the world is counterproductive. It will not work,” Johnson said. “We need to build bridges to communities, to American-Muslim communities right now, to encourage them to help us in our homeland security efforts.”

Presumptive Republican presidential nominee Donald Trump has vowed to suspend immigration from countries with a history of terrorism, including a temporary ban on Muslims coming to the United States.

Trump doubled down on his proposal Monday, one day after Omar Mateen, 29, opened fire in Pulse, a gay nightclub in Orlando and killed 49 people, before police shot him to death. Though Mateen was born in the United States, Trump noted in a speech Monday that he was "born to Afghan parents who immigrated to the United States."

He said Muslim communities must turn over to law enforcement "people who they know are bad," adding "they do know where they are."

Johnson declined to comment specifically on Trump's immigration proposal. He said he sees the need for public vigilance in the case of homegrown extremism, which federal officials now believe is likely the case in the Orlando shooting.

“We’re in an environment now of self-radicalization,” Johnson said of recent attacks in the United States. “It is almost always the case that when someone self-radicalizes, someone close to them sees the sign, which is why we continue to encourage public awareness, public vigilance."

“There’s a role for us to play in building bridges with American-Muslim communities,” he said. “We’re going to encourage the public to be vigilant and to be aware.”

Johnson also defended President Obama against Trump’s implied criticisms that the president is not defending the country.

“Number one, I know from working with him for seven years, the president’s number one priority is protection of the American people, protection of the homeland,” Johnson said. “I know that from my Defense Department experience and now my Homeland Security experience.”