In taking the case this term, the court makes it likely it will issue its ruling by the end of June, when the justices break for the summer.
In December, in a sign that the Supreme Court may be more receptive to upholding the September order, the court allowed it to go into effect as the case moved forward.
The latest travel ban says that the countries "remain deficient at this time with respect to their identity-management and information-sharing capabilities, protocols, and practices".
The justices' decision to hear the case follows a series of lower court rulings against the third version of the ban, which is meant to block citizens of countries deemed security risks from entering the United States. The court put that order on hold, however, in deference to the Supreme Court.
Justice Department officials have said Alsup's decision could keep DACA in place for more than a year without Supreme Court review.
The New York Times reported that in September past year a USA court ruled that the ban was tainted by "religious animus (hostility)" and was not adequately justified by national security concerns.
In court papers, US Solicitor General Noel Francisco, arguing for the Trump administration, said the president has "broad authority to suspend or restrict the entry of aliens outside the United States when he deems it in the nation's interest".
The ban places varying levels of restrictions on foreign nationals from eight countries: Chad, Iran, Libya, North Korea, Syria, Venezuela, Somalia and Yemen.
In June, the Supreme Court allowed that version of the policy to take partial effect.
The appeals court ruled that Trump had exceeded the authority Congress had given him over immigration and had violated a part of the immigration laws barring discrimination in the issuance of visas.
The law does not "surrender to the president a boundless authority to set the rules of entry and override the immigration laws at will", Katyal said in court papers.
They prevailed before a US District Court in Hawaii and before a three-judge panel of the 9th US Circuit Court of Appeals in San Francisco. She suggested that it was by threatening to withhold grants and "conscripting" city police to enforce federal laws.