A federal appeals court in Virginia is holding a crucial hearing to scrutinise a lower judge's ruling that dealt Trump a blow by freezing his second attempt to close US borders to citizens of Iran, Libya, Somalia, Sudan, Syria and Yemen for 90 days.
The challenge for Jeffrey Wall, a Justice Department lawyer representing the administration, will be to persuade judges that the proposed restrictions on entry to the United States fall within established presidential authority.
Wall and his team must also show that the travel rule does not amount to a so-called "Muslim ban," which Trump had threatened to impose while running for office.
Perhaps more difficult, Wall must demonstrate that the rules are "vital" to national security - an assertion weakened as time passes with no known evidence of a serious terror threat to the country.
Trump has often said, while offering no proof, that immigration contributes to US criminality.
Given the public importance of the case and the need for a timely decision, the Fourth US Circuit Court of Appeals in Richmond will head straight for a full-court, or "en banc" hearing - bypassing the usual initial three-judge panel - for the first time in a quarter-century.
The court has 15 active judges, but two have recused themselves over potential conflicts of interest, including conservative judge J Harvie Wilkinson, Wall's father-in-law.
Once considered the most conservative appeals court in the country, the Richmond court now has nine judges named by Democratic presidents including Barack Obama, according to Carl Tobias of the University of Richmond School of Law.
Nevertheless, the outcome remains unpredictable.
First attempt blocked
A lower federal court judge in Maryland had issued a nationwide block on the ban's core provision concerning travel from the short list of countries, saying the order raised the prospect of religious bias against Muslims.
That decision came just after a broader one issued in Hawaii that halted both the travel ban and a 120-day suspension of the US refugee admissions program.
The scope of Trump's revamped ban, signed in early March, was reduced from his original January effort, which blocked travelers from seven-majority Muslim countries, including Iraq, as well as all refugees.
The first decree - which prompted mass protests and sowed chaos at US airports - was blocked by a court in Washington state on the grounds that it violated the US constitution's prohibition of religious discrimination, a ruling that was upheld on appeal.
The modified version removed Iraq from the ban, but ran into the same objections.
Although the travel rule does not explicitly mention Muslims, US District Judge Theodore Chuang of Maryland accepted arguments that Trump's history of anti-Muslim rhetoric presented "a convincing case" that the second executive decree amounted to "the realization of the long-envisioned Muslim ban."
Trump has vowed to fight the "flawed" ruling all the way to the Supreme Court -- to which he recently appointed conservative justice Neil Gorsuch -- describing it as "unprecedented judicial overreach."
A panel of three federal judges will review the Hawaii judgment on appeal later this month.
Appeal fate uncertain
Chuang issued his nationwide ruling in March over a complaint filed by civil rights and refugee advocacy groups, including the American Civil Liberties Union (ACLU), with support from a dozen Democratic-leaning states, many of them in the US West.
The complainants will be represented in Richmond by ACLU lawyer Omar Jadwat, who has called the proposed ban "an unprecedented violation of the fundamental constitutional principle that the government may not disfavor any particular religion."
The Justice Department's case has the backing in Richmond of around a dozen Republican-led states.
Tobias, the law professor, said it could take anywhere from one to six months for the court to issue a ruling -- a task made more complicated by the need to deal with the varying opinions of the large number of judges.