McConnell has thrown his support behind Trump, though a number of Republican leaders, including House Speaker Paul Ryan, have not pledged their unqualified endorsement of the presumptive Republican presidential nominee.
McConnell said he does not agree with many of the things Trump said, but added that he believes the country needs a new direction. He said the Constitution has the ability to keep Trump in check.
"I do think that the Constitution and the traditions of this county constrain all of us — those of us in Congress and those of us in the White House — from some of our impulses, shall I say, that we'd like to pursue."
McConnell said he would like to see "a more thoughtful Trump" who sticks to a script to outline specific policy points.
Trump should reverse his "inflammatory" statements about Hispanics, McConnell said. Trump notoriously characterized Mexican migrants as criminals and rapists last year, and has said he would force Mexico to pay for a border wall.
McConnell said he agrees with Trump that the border should be better secured but criticized him for his "gratuitous" attack on New Mexico Gov. Susana Martinez, the nation's first Latina governor and chairwoman of the Republican Governors Association.
At a campaign event in the state, Trump accused Martinez of allowing Syrian refugees to settle in New Mexico and blamed her for economic problems there. He made the comments after Martinez declined to endorse him and to attend his rally in Albuquerque.