White House says the report, which found 'country of origin' as an unreliable indicator of terrorism, is incomplete.
The president delivered a greatest hits set, boasting of policy goals and repeating criticisms of the judiciary, Democrats and the press.
Director of Homeland Security also says people caught on airplanes when the new order goes into effect will be allowed into the U.S.
Activists called on immigrants to stay home from work, avoid shopping and skip classes in "A Day Without Immigrants," an effort to highlight the vital role they play in American society.
The presidential order imposed a temporary ban on travelers from seven predominantly Muslim countries, but a federal judge has barred enforcement of the order while the court considers a challenge brought by Washington state.
Policy aide continues the administration's attacks on the judiciary, declines to detail next legal steps.
The court's wide ruling leaving Trump's executive order suspended is notable for the legal issues it did not touch.
The enforcement actions took place in Atlanta, New York, Chicago, Los Angeles and surrounding areas.
The White House is not ruling out the possibility of rewriting Trump's Jan. 27 order in light of the actions by a federal judge in Seattle and an appeals court in San Francisco that put the directive on hold.
Kennedy is a conservative justice who sometimes joins the court's four liberals and often casts the deciding vote in close cases.
Shortly after the ruling, Trump tweeted: "SEE YOU IN COURT, THE SECURITY OF OUR NATION IS AT STAKE!"
For more than an hour, people around the United States listened to arguments from attorneys for the U.S. government and Washington state, which sued to challenge Trump's executive order imposing the ban.
The Trump administration has said the ban would help prevent terrorism but opponents assailed it as unconstitutional.
The attorneys general of Pennsylvania, North Carolina and Iowa - key states for Trump in his presidential election victory - say they signed on to the legal action seeking to overturn the travel restrictions because of the potential impact of the presidential order on their states.
A three-judge panel of the 9th U.S. Circuit Court of Appeals in San Francisco heard arguments on Tuesday on the Trump administration's challenge to a lower court ruling putting the temporary travel ban on hold. The appeals court said it would rule as soon as possible but not on Wednesday.
When the travel ban was in place from Jan. 28 to Feb. 4, bookings to the United States dropped 6.5 percent, including an 80 percent slump in reservations from the seven countries listed on Trump's order and a 13.6 percent drop from Western Europe.
"I actually can’t believe that we’re having to fight to protect the security, in a court system, to protect the security of our nation," Trump said at an event with sheriffs at the White House on Tuesday.
The state's top Democrats called Trump cruel and his proposals unconstitutional after the businessman-turned-politician threatened to withhold federal funding from the most populous U.S. state if lawmakers passed a so-called sanctuary bill.
The 9th U.S. Circuit Court of Appeals in San Francisco on Monday asked lawyers for the states of Washington and Minnesota and the Justice Department to argue whether the ban should remain shelved. The court set oral argument for 3 p.m. PST on Tuesday.
The companies—including Apple Inc, Google Inc and Microsoft Corp—banded together late on Sunday to file a "friend-of-the-court" brief with the 9th U.S. Circuit Court of Appeals in San Francisco arguing that the ban "inflicts significant harm on American business."
The government now has until 3 p.m. PST on Monday to submit additional legal briefs to the 9th U.S. Circuit Court of Appeals in San Francisco in support of Trump's order. A decision either way may ultimately result in the case reaching the U.S. Supreme Court.
Canadian advocacy organizations are bracing for a greater influx of asylum-seekers, driven in part by the contrast between the ruling Liberal government's acceptance of Syrian refugees in Canada with Trump's anti-foreigner rhetoric.
The ruling was a victory for the Trump administration and a setback for state authorities and advocacy groups that are aiming to overturn last week's executive order.