The Hindu American Foundation (HAF) expressed concern over the practical and legal implications of the executive order affecting immigration policy and its detrimental impact on refugees and legal immigrants.
"Implementing any sort of religious preference for admittance would be fundamentally unconstitutional and any permanent blanket ban based on national-origin would be illegal," HAF executive director Suhag Shukla said.
"President Trump's statements immediately after signing the executive order, in which he emphasised that Christian refugees would carry priority, does elicit serious concerns," he said.
Trump signed an executive order last week suspending the arrival of all refugees for at least 120 days, Syrian refugees indefinitely, and barring citizens from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen for 90 days, fulfilling one of his central campaign promises.
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On the other hand, the Republican Hindu Coalition (RHC), which had campaigned for Trump during the general elections announced its full support to the executive orders signed by Trump.
"A firm stance against terror is one of the pillars of our organisation and one of the central tenets of the Trump campaign, and we fully support our Commander-in-Chief taking the necessary steps to protect our country," he said.
RHC board members in a meeting also urged the Trump Administration to include Afghanistan, Pakistan, and Saudi Arabia in the list of seven countries named in the Executive Order.
The group also asked for thorough investigation of green- card holders from the banned countries, in the 90-day period, heightened scrutiny and inspection of all travellers heading to the countries listed in the ban and indefinite suspension of all refugees from entering the United States.