Silicon Valley heads have slammed US President Donald Trump's temporary ban on refugees and many Muslims from entering the United States, fearing it could prevent them from accessing a global reservoir of talent.

The sweeping immigration crackdown moved many tech bosses to criticize measures that could impact sector employees.

"Apple would not exist without immigration, let alone thrive and innovate the way we do," said Tim Cook in a memo to staff obtained by AFP.

The company's founder Steve Jobs was the son of a Syrian immigrant.

Netflix CEO Reed Hastings called the president's first week in office "very sad," saying in a Facebook post that "Trump's actions are hurting Netflix employees around the world, and are so un-American it pains us all."

"It is time to link arms together to protect American values of freedom and opportunity."

Nearly 200 Google employees are directly impacted by the measures, according to an internal memo from CEO Sundar Pichai.

"We're concerned about the impact of this order and any proposals that could impose restrictions on Googlers and their families, or that could create barriers to bringing great talent to the US," said the head of the internet giant.

Trump's hardline executive order, signed Friday, suspends the arrival of refugees for at least 120 days, and for the next three months bars visas for travelers from seven Muslim-majority countries: Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen.

- 'Best and the brightest' -

Immigration law specialist Ava Benach -- who told AFP she has been flooded with calls from clients -- said those already in the US should stay put, and those abroad risk being blocked from boarding aircraft.

"I would advise against leaving the US because I don't believe that they will be able to return," she said.

As resistance to the temporary immigration restrictions mount, a US federal judge on Saturday ordered authorities to stop deporting refugees and other travelers stuck at US airports.

US District Judge Ann Donnelly's decision to issue a temporary stay -- which stopped short of ruling on the constitutionality of Trump's order -- came after dozens of people were detained at US airports following Trump's actions.

"As an immigrant and as a CEO, I've both experienced and seen the positive impact that immigration has on our company, for the country, for the world" said Microsoft head Satya Nadella, who is of Indian descent.

The company had warned Thursday that immigration restrictions could impact its ability to fill research and development positions.

Globalization has been a boon for Silicon Valley, which employs a significant population of foreign engineers. Some 250,000 Muslims live in the San Francisco Bay Area, according to the Council on American-Islamic Relations.

"Internet companies in particular thrive in the US because the best and the brightest are able to create innovative products and services right here in America," said Michael Beckerman, the head of a leading industry lobby group.

Trump met last month with a handful of America's most powerful tech executives -- a bid to mend fences with a largely pro-Democrat industry.

No announcements were made following the summit, however.

In the short term, many tech companies are offering legal assistance to staffers impacted by the executive order.

"We are assessing the impact on our workforce and determining how best to protect our people and their families from any adverse effects," a Facebook spokesperson told AFP.

Chris Sacca, a major financial backer of the sector, vowed to donate $150,000 to the American Civil Liberties Union, an organization that has hit the executive order with legal challenges.

Uber CEO Travis Kalanick vowed to raise the issue at a meeting next week of Trump's business advisory council, which the executive is a part of.

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