"The Executive Order is an unconstitutional infringement upon the rights of Muslims. It inflicts significant harm on the American Muslim community and American Muslim professionals," the groups said in their legal brief filed before US 9th Circuit Court of Appeals.
"It threatens American Muslims' ability to practise their professions in the United States; it threatens American Muslims who live, work, travel and have families abroad; and it subjects Muslims to a damaging stigma," said the collective legal filing.
Urging the court to deny the Government's Motion for extraordinary interlocutory relief, the organisations said Muslim Americans were suffering an additional injury as a result of the stigma that has attached to the community, unfairly and irrationally.
"The intentional and false stigmatisation of Muslims as potential terrorists - even if supposedly limited to Muslims from the 7 majority-Muslim countries expressly included in the Executive Order - will, if not restrained, continue to irreparably harm Amici," it said.
"Muslims have expended their blood, sweat, and tears building and defending the United States," it said, adding that more than 5,000 Muslims serve in the US military, and many have given their lives in recent wars in defense of American interests.
"They also provide necessary healthcare, educate our nation's children, create jobs, and contribute innovation that is an essential driver of our nation's economic growth. Today, Muslims represent one per cent of the US population," the legal brief said.