Keller added that courts should be careful when second-guessing a president's national security determinations, an argument that echoes the administration's view that the judiciary should defer to the president on such matters.
In the United States, many veteran diplomats and officials decried Trump's remarks.
Neal Katyal, a lawyer for the state of Hawaii in a separate case about the executive order, tweeted that Trump is "acting as our co-counsel" by speaking publicly about the "travel ban".
The London attacks on the weekend and a deadly episode in the Philippines last week both prompted a visceral reaction from President Donald Trump, but not one based on facts. He was then harshly criticized when he appeared to misconstrue a statement while launching an attack on London Mayor Sadiq Khan, who said there was "no reason to be alarmed" by the visible increase in police activity in the wake of the attacks.
When asked how relevant Trump's tweets are, White House spokeswoman Sarah Sanders said "they matter in the sense that they give him a communications tool" but said "the media obsesses over every period, dot".
The states said Mr. Trump has broad powers under the law to decide whom to admit, and said USA law is replete with examples of the government singling out groups for different treatment in immigration contexts.
Yet the president said on Monday that the order is exactly that.
"If you're going to see something and say something, it has to be followed by, do something", she said.
"This injunction is contrary to law, and it denies the federal government - under a statutory regime crafted by the representatives from the States in Congress - the latitude necessary to make national-security, foreign-affairs, and immigration policy judgments inherent in this country's nature as a sovereign", the brief reads.
Third, and perhaps most troubling, what does Trump mean when he calls for the Justice Department to seek a "much tougher version"?
British authorities say that have identified the three attackers but have not revealed that information publicly. "His lawyers tried to justify it by saying it wasn't a travel ban, that it was just extreme vetting", Cardin told CNN.
Conway again stressed, however, that the president's tweets "seriously undermine" his own administration's agenda, a point that has also been made by other legal experts. The directive was stalled in federal courts, with judges ruling that it was a discriminatory travel ban.
Defending the executive order - which is a revision of a stricter one signed in Trump's first days as president - has been such a delicate process that lawyers for the Justice Departments have frequently avoided using the words "travel ban" in legal briefs.
The lower court's order was upheld by the US Court of Appeals for the Ninth Circuit on Feb 9.