The administration of US President Donald Trump on Saturday began the process of appealing the decision of a federal judge who suspended the application of an immigration ban to citizens of seven Muslim-majority countries, the media reported.

In a short document presented to the 9th Circuit Court of Appeals, based in San Francisco late Saturday, Trump and his cabinet formally appeal the judicial decision that has temporarily blocked the controversial executive order and has reopened the country's doors to millions of immigrants and refugees, Efe news reported.

The Notice of Appeal was made in the name of Trump, Homeland Security Secretary John Kelly, Secretary of State Rex Tillerson, and the United States of America.

The parties above appealed to the 9th Circuit Court of Appeals the decision to restrict the application of Trump's executive order is to protect the country from terrorist threats, according to the Notice of Appeal.

The document has begun a process of appeal that, according to legal experts, will be followed by an application to suspend the judicial order that blocked the immigration ban, and a report with arguments on why, in the government's view, the courts should grant them this petition.

The appeal follows a late Friday decision by US District Court Senior Judge James L. Robart, appointed by former President George .W. Bush, when he granted an injunction by blocking enforcement of Trump's executive order instituting the travel ban, acting at the request of Washington state Attorney General Bob Ferguson, whose office said that the temporary restraining order applies nationwide.

Trump's policy banned travel to the US from seven Muslim-majority countries for 90 days, suspended all refugee entry to the US for 120 days and indefinitely suspended entry for Syrian refugees.

If the 9th Circuit Court of Appeals rules against the Trump government, the case could go to the Supreme Court, something many experts consider likely.

Asked at a gala in Florida about whether he was confident his administration would prevail in the appeal, Trump replied, "We'll win. For the safety of our country, we'll win", CNN reported.

The three judges who will likely hear the appeal are: Judge William Canby, who was appointed by President Jimmy Carter; Richard Clifton, who was appointed by Bush; and Michelle Friedland, a President Barack Obama appointee.

Although it is unclear what form of relief the Justice Department will seek, the White House said on Friday that it wants an "emergency stay" of Robart's order.

Also on Saturday, the Department of Homeland Security announced it had suspended all actions to implement the immigration order and would resume standard inspections of travellers as it did prior to the signing of the travel ban.