Attorneys for Gold Star father Khizr Khan filed his brief in San Francisco where the 9th US Circuit Court of Appeals is considering an appeal to the ruling by US District Judge Derrick Watson.
Khan's son, Humayun Khan, was a Muslim US Army captain who was killed in 2004 by a suicide bomber in Iraq. Humayun was posthumously awarded a Bronze Star and a Purple Heart.
During last year's Democratic National Convention, Khan drew national attention when he criticised the anti-Muslim rhetoric of then-Republican nominee Trump.
Trump took to Twitter to criticise Khan, saying the fallen soldier's father had “viciously attacked” him.
Days after his inauguration, Trump issued an executive order restricting travel from seven predominantly Muslim countries. A federal judge blocked the order in February.
In March, Trump issued a revised travel ban order that blocks new visas for people from six Muslim-majority countries and temporarily halts the US refugee programme.
Watson issued a temporary restraining order against the revised ban after the state of Hawaii filed a lawsuit challenging it.
Hawaii says the policy discriminates against Muslims and hurts the state's tourist-dependent economy.
Extending the judge's temporary order until the lawsuit is resolved would ensure the constitutional rights of Muslim citizens across the US are vindicated after “repeated stops and starts of the last two months,” the state has said.
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