A few chief executives joined protests against President Donald Trump's temporary ban on immigration from seven Muslim countries, but a larger group of CEOs remained publicly silent over fears of being targeted by the president, CNBC's Andrew Ross Sorkin said Monday.

The Financial Times' Gillian Tett said on CNBC's "Squawk Box" that she had spoken with CEOs who were privately upset by the executive order but worried about speaking out. "Squawk Box" co-host Sorkin said he had heard the same from his C-level sources.

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"I had similar conversations with executives over the weekend, all of whom ... seemed to be upset about at least the implementation of this program," Sorkin said. "They are scared out of their minds about being attacked ... and what that's going to do for their business."

Tett said the CEOs she contacted were especially worried about the risk of speaking out in the context of Trump's potential backlash — and that of his supporters.

"The danger is twofold: Firstly, the fact that you've got a president who will tweet out statements that can be very damaging to the share price," Tett told "Squawk Box."

"But secondly, of course, you've got a lot of people who agree with what he's doing and who will take revenge against companies whether that's on social media or [via] boycott," she continued.

Tett said she hoped CEOs, especially those with seats on Trump's various advisory councils, would band together to push back on the president's controversial legislation.

"Maybe they should be trying to use some of their joint industry forums. Because people have come out and said, 'Yes, we love parts of [the] economic policies,' but it does not mean you have to endorse everything," Tett said.

"The really key question is, 'Will those CEOs who are now sitting on that advisory council actually use that power or are they just doing it for pure vanity play?" Tett asked.