Two leading GOP senators, John McCain and Lindsey Graham, joined other Republican officials on Sunday in criticizing President Trump's executive order on immigration and refugees.

McCain of Arizona and Graham of South Carolina issued a joint statement saying, "Our government has a responsibility to defend our borders."

“It is clear from the confusion at our airports across the nation that President Trump’s executive order was not properly vetted," the two senators said. "We are particularly concerned by reports that this order went into effect with little to no consultation with the Departments of State, Defense, Justice, and Homeland Security. We fear this executive order may do more to help terrorist recruitment than improve our security."

They continued, "We must do so in a way that makes us safer and upholds all that is decent and exceptional about our nation."

Trump responded in a series of tweets from his personal account, calling the two senators "wrong" and "sadly weak on immigration."

Shortly after the president tweeted, Sen. Bob Corker of Tennessee released a statement to ABC News.

“We all share a desire to protect the American people, but this executive order has been poorly implemented, especially with respect to green card holders,” said Corker. “The administration should immediately make appropriate revisions, and it is my hope that following a thorough review and implementation of security enhancements that many of these programs will be improved and reinstated.”

Corker is the chairman of the Senate Foreign Relations Committee.

House Homeland Security Committee Chairman Rep. Michael McCaul of Texas, an adviser to Trump on counter-terrorism during the presidential campaign, broke with the White House on green card restrictions.

"We should not simply turn away individuals who already have lawful U.S. visas or green cards—like those who have risked their lives serving alongside our forces overseas or who call America their home," McCaul said in a statement.

Some leading Republicans said they support the order but criticized its implementation.

The order signed Friday immediately suspends immigration from seven predominantly Muslim countries in the Middle East and Africa -- Syria, Yemen, Sudan, Somalia, Iraq, Iran and Libya -- for 90 days. It also blocks refugees from entering the country for 120 days; refugees from Syria are barred indefinitely.

"President Trump has finally taken necessary national security and public safety measures regarding refugees and non-immigrants seeking entry," according to a statement from Rep. Raul Labrador of Idaho. But, he said, "Inadequate review and poor implementation of this executive action threatens to undermine otherwise sound policy. I remain a strong supporter of President Trump’s bold efforts to keep America safe, but they must be legally sound and uniformly enforced." look forward to working with the president on these issues."

A handful of other Republicans over the weekend slammed the order, many of them expressing concern that the order is too broad and questioning its effectiveness in reducing the threat of terrorism.

Sen. Ben Sasse of Nebraska, a member of the Senate Armed Services Committee, issued a statement Saturday titled "Border Security and Muslim Nations" in which he said the ban was too far-reaching.

"The president is right to focus attention on the obvious fact that borders matter," he said. "At the same time, while not technically a Muslim ban, this order is too broad."

Sasse, who was critical of Trump during the presidential campaign but now supports him, also questioned if the order was the most effective way to fight jihadism.

"There are two ways to lose our generational battle against jihadism by losing touch with reality," he said. "The first is to keep pretending that jihadi terrorism has no connection to Islam or to certain countries. That's been a disaster. And here's the second way to fail: If we send a signal to the Middle East that the U.S. sees all Muslims as jihadis, the terrorist recruiters win by telling kids that America is banning Muslims and that this is America versus one religion. Both approaches are wrong, and both will make us less safe. Our generational fight against jihadism requires wisdom."

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