“I don't want to criticize them for improving vetting. I think we need to be careful; we don't have religious tests in this country," the Kentucky senator said on "This Week."
In fact, an Iraqi man who worked as an interpreter for the U.S. Army in his home country was detained at Kennedy International Airport in New York City overnight Friday after the president's executive order was signed. He was released after the intervention of civil rights lawyers Saturday.
McConnell told Raddatz of the executive order, “It's hopefully going to be decided in the courts as to whether or not this has gone too far.”
On the topic of Russia, the GOP Senate majority leader said he is "absolutely opposed" to lifting sanctions on the country, something the Trump administration says it is considering.
"If anything, we ought to be looking at increasing them," the Kentucky Republican added.
Trump spoke with Russian President Vladimir Putin on Saturday and a White House readout of the call did not mention the sanctions, which were put in place by the Obama administration for Russia's incursion into Ukraine, annexation of Crimea and cyber-hacking in the 2016 election. But a readout from the Kremlin said the two leaders "underlined the importance of restoring mutually profitable trade and economic connections between the business circles of the two countries."
The Trump White House simply said the call was a “positive” discussion and a “significant start to improving the relationship between the United States and Russia that is in need of repair.”
Senators John McCain and Chuck Schumer have introduced bipartisan legislation to codify those sanctions into law and prevent the White House from removing them without Congress's consent. But McConnell would not say whether he supports such a bill.
McConnell declined to comment on another action by the president -- his memorandum Saturday that reshaped the National Security Council, giving Trump's chief strategist Stephen Bannon a seat at all of the council's principals meetings, but limiting the meetings that the director of national intelligence and the chairman of the Joint Chiefs of Staff can attend.
“I’m not going to give the president advice about how to run these internal agencies,” McConnell said.
The Senate leader previewed the president’s pick for the Supreme Court, which Trump is expected to make Thursday.
“I think we’re going to get a really outstanding nominee, who will be very hard to argue against because the president has been working on this for some time,” he said.