President Donald Trump says he has told US border officials to check people entering America "very carefully", as his travel ban remains suspended.
He said the courts were "making the job very difficult", and should take the blame if something happened.
The federal appeals court on Saturday rejected the Trump administration's request to reinstate the ban.
The ban, affecting people from seven mainly-Muslim countries, was blocked by a federal judge on Friday.
This means that Mr Trump's directive will remain suspended and visa holders Iraq, Syria, Iran, Libya, Somalia, Sudan and Yemen will be allowed to enter the US until the full case has been heard.
The White House and two US states challenging the ban have been given a deadline of Monday to present more arguments.
President Trump on Sunday ramped up his criticism of Seattle Judge James Robart, who blocked the ban, and the country's judiciary.
In a series of tweets, Mr Trump said: "I have instructed Homeland Security to check people coming into our country VERY CAREFULLY."
"Just cannot believe a judge would put our country in such peril. If something happens blame him and court system. People pouring in. Bad!"
The president earlier called Judge Robart's ruling "ridiculous", described him as a "so-called judge".
US border checks
- All persons arriving at a US port of entry are inspected by Customs and Border Protection (CBP) officers
- Visitors must have valid US visas or hold 'Green Cards' that authorise them to live and work in the US permanently
- Travellers under the Visa Waiver Program must apply for authorisation via ESTA (Electronic System for Travel Authorization) before their visit
- Visitors must complete declaration forms
- Travellers may have their fingerprints and photos taken
- CBP officers may also ask to inspect luggage or personal items
- CBP uses biometric technologies to verify travellers' identities
- Travellers from certain countries can use Automated Passport Control (APC)
In its appeal, the Justice Department said Judge Robart had overreached by "second guessing" the president on a national security matter.
It also argued that only the president could decide who can enter or stay in the US.
Media caption"The American people are very accustomed to this president speaking his mind" - Vice-President Mike Pence
The two states challenging the restriction - Washington and Minnesota - argued that the ban was unconstitutional and denied people with valid entry documents the right to travel without due process.
It also violated freedom of religion rights by appearing to target Muslims, they said.