The states’ brief tells the Supreme Court that the order did not unconstitutionally single out Muslims and was needed to protect national security.
The Trump administration has argued that the travel ban is needed to prevent terrorism in the US.
The judges all questioned the neutrality of the ban, specially since Trump has never retracted previous comments about wanting to impose a ban on Muslims.
US Chief justice Roberts is particularly concerned about the government’s claim that it can revoke citizenship through criminal prosecution for trivial lies.
Justice Anthony Kennedy’s retirement would give Trump a further chance to shape the Supreme Court, after his first nominee Neil Grouch was sworn in this week.
With Neil Gorsuch aboard, the court has five conservative justices and four liberals, a majority that could be pivotal in deciding a range of issues including abortion and gun control.
If the Supreme Court rules that Title IX protects transgender students, the decision would become the law of the land, binding the Trump administration and the states.
The battle over abortion rights is set to have crucial impact on the presidential elections as the public opinion is split over the matter.
The Republican-led Senate had been for long opposing Obama’s policy for giving recognition to the immigrants.
President Obama hailed the verdict upholding the consideration of race in college admissions.