The administration also moved to assure nervous counterparts in the UK and elsewhere about how their citizens would be affected.
Trump, who spent part of the afternoon at a staff screening of the animated movie Finding Dory at the White House, emerged to say on Twitter that McCain and Graham's statement was "wrong — they are sadly weak on immigration." Senators should focus their energies on Islamic State, illegal immigration and border security, he said, "instead of always looking to start World War III".
In a statement from the White House and on Facebook, Trump repeated that the move was "not a Muslim ban," and said his policy was "similar to what President Obama did in 2011 when he banned visas for refugees from Iraq for six months."
"I have tremendous feeling for the people involved in this horrific humanitarian crisis in Syria," Trump said in the statement.
World leaders including Canadian Prime Minister Justin Trudeau and German Chancellor Angela Merkel have denounced the move. Merkel expressed her concerns about the temporary ban during a call with Trump on Saturday. Australia on Monday said it's asking the Trump administration to ensure its citizens are exempt from the ban, after US officials moved to reassure Canada and the UK.
A federal judge in Boston on Sunday became the latest to curb Trump's immigration order, directing customs officials at the city's Logan International Airport to let passengers from the seven countries with valid visas go on their way. Protests were held at numerous airports and cities around the country, including one outside the Trump International Hotel in Washington.
Signs at the Washington demonstration included "No Muslim Ban" and "The Pilgrims were undocumented". Protesters led chants that included "No hate, no fear, refugees are welcome here".
"I'm here because I'm very frightened about Trump's actions against immigration," said Lisa Richard, 59, who lives in Virginia. Richard also protested at Dulles International Airport on Saturday night. "This is as anti-American as it could be," she said.
Trump told his almost 23 million Twitter followers on Sunday morning: "Our country needs strong borders and extreme vetting, NOW. Look what is happening all over Europe and, indeed, the world — a horrible mess!"
Judges temporarily blocked the administration from enforcing portions of his order to halt immigration and entry of citizens of Syria, Iraq, Iran, Sudan, Somalia, Yemen and Libya. Under the order, the admission of refugees would also be suspended for 120 days.
Sudan's foreign minister, Ibrahim Ghandour, said came the ban comes as the two countries started to work more closely to combat terror and only two weeks after Obama lifted decades-old sanctions on the North African country.
"We feel sorry that the decision was taken at a time we started cooperating and the sanctions were lifted," Ghandour said in an interview in the Ethiopian capital, Addis Ababa, where he's attending an African Union summit. We'll wait "until the executive decision passes and see what is next after that and then we'll act accordingly".
White House spokesman Sean Spicer said on ABC's This Week programme that 109 people held by immigration authorities on Saturday were simply "slowed down" in entering the US, he said, because "the safety of the American citizens, the safety of our country has got to be paramount".
The judges' moves on Saturday followed a day when a number of students, refugees and dual citizens were stuck overseas or detained, and some businesses, including Google, warned employees from those countries not to risk leaving the US.
Senate Majority Leader Mitch McConnell expressed opposition to "religious tests" for immigration restrictions.
"It's hopefully going to be decided in the courts as to whether or not this has gone too far," McConnell, a Kentucky Republican, said on ABC.
"I don't want to criticise them for improving vetting. I think we need to be careful. We don't have religious tests in this country."
In their joint statement, McCain and Graham said they were "concerned by reports that this order went into effect with little to no consultation with the Departments of State, Defense, Justice, and Homeland Security".
"Ultimately, we fear this executive order will become a self-inflicted wound in the fight against terrorism," the senators said.
Friday's executive order was reviewed by the Department of Justice's Office of Legal Counsel before being made final, according to a White House aide.
DHS said in a statement late Sunday that it was, and will remain, "in compliance with judicial orders" and was working with the departments of Justice and State to implement Trump's executive order.
"We are committed to ensuring that all individuals affected by the executive orders, including those affected by the court orders, are being provided all rights afforded under the law," the agency said. It also issued a two-page fact sheet on the order.
Trump returned to Twitter to say that "Christians in the Middle East have been executed in large numbers. We cannot allow this horror to continue!"
In an interview with the Christian Broadcasting Network, Trump said Christians should be a priority in a revamped refugee programme.
"It was almost impossible" for Syrian Christians to enter the US, Trump said.
- With assistance from Elizabeth Dexheimer
