Mr Trump also said he had instructed border officials to check people entering America "very carefully".
President Trump on Sunday ramped up his criticism of 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. The courts are making the job very difficult!"
"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".
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 Seattle's federal judge on Friday.
This means that Mr Trump's directive will remain suspended and visa holders from 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.