In a press release, US attorney general Jeff Sessions declared that the government would also take what he described as the "rare step" of going directly to the Supreme Court - a procedure known as "certiorari before judgment".
The petition is highly unusual, as the government bypassed the 9th U.S. Circuit Court of Appeals and asked the justices to hear the case in the near future - but the administration argues that the move is justifiable, as the lower court order "requires the government to sanction indefinitely an ongoing violation of federal law being committed by almost 700,000 aliens".
"We have always known this case would ultimately be decided by the United States Supreme Court", said state Attorney General Doug Chin of Hawaii, which has repeatedly fought the travel bans.
"The district court has entered a nationwide injunction that requires DHS to keep in place a policy of non-enforcement [of immigration laws] that no one contends is required by federal law and that DHS has determined is, in fact, unlawful and should be discontinued", the Justice Department lawyers argue in making their case for why the district court's ruling should be reviewed and overturned.
The Supreme Court will now consider on January 22 two PILs seeking independent probe into the death of Mumbai's special CBI judge B H Loya, who was then hearing the Sohrabuddin Sheikh encounter case.
The most recent version of Trump's "enhanced vetting" order, announced in October, prohibits travel to the United States by most people from Chad, Iran, Libya, Somalia, Syria and Yemen.
Those challenging the travel ban have argued that it was motivated by Trump's enmity toward Muslims, pressing that point in court with some success by citing statements he made as a candidate and as president.
Trump's initial travel ban, decreed a week after he took office, triggered chaos out at United States airports, with travelers detained upon arrival, and nationwide protests against a measure seen as discriminatory - though Trump said it aimed to keep out extremists.
The Supreme Court, which is tackling a series of consequential cases during its current term, signaled on December 4 it was likely to uphold the policy.
At times as the lawsuits against the Trump initiatives have unfolded in the lower courts, there have been temporary rulings that the presidential order would likely be found to be an unconstitutional "Muslim ban".
The latest ban was introduced on September 24 after what Francisco called an "extensive, worldwide review" to determine which foreign governments provide information required by the United States to vet those seeking entry. The law also prohibits discrimination on the basis of nationality.
"The immigration laws do not grant the President this power", Katyal said.
Although lower courts have ruled against Trump over this three travel bans, the Supreme Court has given him a friendlier reception.
Trump's lawyers say the refinements made to the travel ban, including the decisions over the previous year to drop the Muslim-majority countries of Iraq and Sudan, show the policy isn't aimed at a particular religion.