McCain, R-Ariz., called Trump's decision "the wrong approach" to immigration policy.
"I strongly believe that children who were illegally brought into this country through no fault of their own should not be forced to return to a country they do not know," McCain said in a statement. "The 800,000 innocent young people granted deferred action under DACA over the last several years are pursuing degrees, starting careers and contributing to our communities in important ways."
McCain said that although he disagreed with President Barack Obama's use of an executive order, reversing the policy now would be "unacceptable." He vowed to work with other lawmakers to pass comprehensive immigration reform.
Other Republicans also promised to push for comprehensive immigration reform.
Sen. Jeff Flake called executive actions a poor substitute for permanent legislation in a tweet storm. "The ball is back in Congress' court where it belongs," he said, in a tweet.
"Congress must act immediately to pass permanent, stand-alone legislation to lawfully ensure that children who were brought here...
by their parents, through no fault of their own, are able to stay and finish their education and continue to contribute to society."
House Speaker Paul Ryan criticized Obama's executive order and said he welcomed the opportunity to pass legislation.
"It is my hope that the House and Senate, with the president's leadership, will be able to find consensus on a permanent legislative solution that includes ensuring that those who have done nothing wrong can still contribute as a valued part of this great country," Ryan said in a statement.
Democrats were quick to condemn Trump's decision and urge Congress to act.
Sen. Elizabeth Warren tweeted: We cannot sit back while our family, friends & neighbors are driven out of their homes. We must fight to protect Dreamers & #DefendDACA.