"Congress has granted the president sweeping power to suspend or restrict entry of aliens overseas", U.S. Solicitor General Noel Francisco said in court papers.
Josh Blackman, a law professor at the South Texas College of Law in Houston, believes the justices will find that the travel ban passes legal muster.
Hawaii is leading the challenge at the high court.
The travel ban is the first Trump policy to undergo a full-blown Supreme Court review.
Kennedy, a conservative who sometimes joins the liberals in major rulings, pushed back on the notion pressed by the challengers that the ban was permanent, noting that the policy includes a requirement for ongoing reports that could potentially lead to the removal of a targeted country.
The justices voted in December to allow the policy to take full effect pending their full consideration.More news: Former Port Authority Official Badgers New Jersey Cops Over Traffic Stop
Among those inside the courtroom Wednesday was White House counsel Don McGahn, seated next to former Supreme Court justice Thurgood Marshall's widow, Cecilia.
Generally when the Supreme Court overturns a lower court's injunction, he said, it means the justices also end up reversing the final decision.
The Supreme Court is considering whether the president can indefinitely keep people out of the country based on nationality.
Challengers of the ban argue that it is "an order without parallel in our nation's history" and that it amounts to a "sweeping and unilateral order that purports to ban over 150 million aliens - the vast majority of them Muslim - from entering the United States". The state's lawyer, Neal Katyal, called the travel ban an "unprecedented assertion of power".
"This is an out-of-the-box kind of president in my hypothetical", she said.
The Justice Department argues Trump's statements as a candidate carry no weight because he was not yet president.More news: Saquon Barkley goes sneaker shopping with Complex
From the other side, Sotomayor told Francisco she doubted that the president has "the authority to do more than Congress has already decided is adequate" under immigration law.
The court will consider the third iteration of Trump's travel ban, issued last fall, which barred various travelers from eight countries, six of them with Muslim majorities.
People began lining up days in advance for one of the roughly 50 seats the court typically sets aside for members of the general public. "Ever." and "Refugees Welcome", among other things. It's the first time this term the court has released same-day audio.
Trump's travel ban - the third version of a policy he first sought to implement a week after taking office in January 2017 - blocks entry into the United States of most people from Iran, Libya, Somalia, Syria and Yemen.
Hawaii, several individuals and a Muslim group challenged the latest ban's limits on travel from the predominantly Muslim nations; they did not object to the portions concerning North Korea and Venezuela. It also affects two non-Muslim countries: blocking travelers from North Korea and some Venezuelan government officials and their families. That happened earlier this month, when Trump removed Chad from the list of restricted countries.
Trump's campaign pledge to shut down Muslims' entry into the US, his presidential tweets about the travel ban and last fall's retweets of inflammatory videos that stoked anti-Islam sentiment all preceded the justices' questioning of Francisco, defending the ban, and Katyal, the former acting solicitor general under President Barack Obama.More news: Pelicans to face Golden State Warriors in second round of National Basketball Association playoffs
"It's absolutely vital that the president maintains the ability to determine who enters the country from a security standpoint", he said. Francisco also has said in written arguments that Trump's September proclamation laying out the current policy comports with immigration law and does not violate the Constitution because it does not single out Muslims.